Stipend vs employment contract in Saxony (Germany) I have found some information online regarding the differences between going for a PhD with an employment contract or a stipend, in Germany. The differences are mostly related to the time you can research stuff not exactly in line with your thesis, social safety and mandatory working hours. The salaries do not seem to change much.

In my case, I was offered the option to choose between stipend and employment contract for a post-doc position, not a PhD, in the German state of Saxony. I couldn't find much about this topic online. My field is physics, I'm 29, unmarried and no children. This is my first post-doc.

What are the fundamental differences? I'm particularly scared of the mandatory working hours associated to the employment contract option. I do work a lot, often from home, but I really value the freedom I currently have of simply skipping a day at work and working on a weekend, etc.
Recommendations: 


Calculate whether the scholarship offer is a fair offer (see below). 
If not, the employment contract is the only feasible option.
Check whether the institution insinuates that a scholarship is basically the same as the employment contract wrt. to your contractual duties. If so, that is (at least to me) a big red flag about an inclination to institutional abuse of power. And that means that you should also think carefully whether you want an employment contract with that institution.  
At least, check the customs of your group-in-spe and how much freedom postdocs have there. Your group leader may be in a more or less good position to give you more freedom than the institution normally does. 




Note I use "scholarship" here for the German Stipendium. AFAIK, the English stipend/scholarship do not directly translate to the German Stipendium.



Others have already told you that the social insurance treatment is very different. I'd like to expand a bit further on this. 

IMHO the best (fair) starting point for comparison is to consider the scholarship equivalent to the employer's gross (Arbeitgeberbrutto) of an employment contract for which no income tax is due. 


Scholarships for scientific work are not subject to income tax
Check with my tax office that the particular contract that is offered fulfills their criteria for this, though. One of the criteria is to check whether the contract is actually a scholarship and not an employment contract.  
Health and long-term care insurance is mandatory whether you are employee or not. 

Not being an employee and being young and without family, you may be able to get a cheaper private health insurance than the governmental one.  

You can also go with the governmental health insurance (called "voluntary" or sometimes "voluntary mandatory" tariff, there will be no health check for this). In that case, your fee will be the same percentage as employer + employee percentages together, approximately 1/6 of your income. But while for an employee only the wage is counted, in the voluntary tariff all sources of income count (small time freelancing as a side line, interest/dividends, rental income?).  

If you are coming from a foreign contry, you may be able to bring a health insurance with you. Health insurance for young academics going to work abroad for a while can be surprisingly cheap.
Unemployment insurance is for employees only. You don't have to pay, but you'll also not be eligible for benefits later on. Currently relevant: these benefits include the Kurzarbeitergeld (short-time compensation). OTOH, a scholarship is not bound to working hours, so the scholarship is anyways paid also if you cannot work due to your workplace being closed because of SARS-CoV-2.
I'd argue that you should put at least a comparable amount aside into an additional emergeny fund.
Pension cass is not mandatory. If you want, you can make voluntary contributions, though, and in that case you can largely decide how much you want to pay into pension cass. Such contributions will count both as contribution years as well as according to the amount paid in.
Again, if you choose not to contribute it is probably a good idea to put at least a corresponding amount (between 1/6 and 1/5 of your income) into your own retirement fund.

The pension cass is also responsible to decide whether a given contract is an employment contract or a scholarship - you can ask them for clarification. If they find it is not a scholarship*, there will be a big stink though, since you just exposed your institute-in-spe trying to commit social insurance fraud.


Whether these points put you at an advantage or a disadvantage will depend on your actual circumstances.

(I've had the luck to get a scholarship as PhD student that was actually fair according to this calculation - but it was the only one scholarship program that paid so much that I'm aware of. When I write "I'd argue": acually I have been arguing when that funding agency was cutting the scholarships that a fair comparison would tell the scholarship holders that while it is ultimately their own decision, they should consider the social insurance percentages as ballpark for how much they should put aside for rainy day/pension)


You will not be covered by the work accident insurance mandatory for employees. Part of this is not a disvantage: as long as your institute has employees, the place anyways needs to be safe according to work accident insurance rules.
But: you have a work accident there will be differences to you. Your treatment will be paid by your normal health insurance. But work accident insurance patients may be treated preferentially wrt. waiting times (OTOH, there is no free choice to which doctor to go initially). This includes any accidents you have on the direct way from home to work and back.




There are usually some specific advantages for scholarship holders over employees:


Many scholarships have associated training programs on various topics
Many scholarships give you additional project/book/travel money that noone but you can spend. In that respect it's like a mini-grant for you only.
You are more free in your scientific work than an employee.
Of course, many professors leave great freedom to their employed postdocs, but not all do. A scholarship legally means that you must be free in this respect.
@mmeent has a point that some institutions have a bad reputation of abusing scholarshiops, though: not only of not paying what would be fair according to the calculations above, but also by insinuating that the scholarship holders are bound to directions of the institute like employees. In other words, abuse of power.
Since you are not an employee, e.g. the copyright of software you write stays yours - it will not be automatically transferred to the university.
Same for inventions.


Again, many institutes are happy if their postdocs take software they wrote with them and go on taking care of it rather than risking more abandonware - I had one such institute that put the software under a FOSS license for this reason and I still take care of the software almost 10 years later. But I've also been at an other institute where the standard license is best described as "no bit leaves the house". 



Since you may change to academic employment: at least within Germany the wages depend on your relevant work experience. Scholarship may not be counted automatically by prospective employers, but you can ask your institute to certify (write a letter) that they consider your scholarship as equivalent to you working. 



Employment contract


  mandatory working hours  associated to the employment contract


In the past, this again was something that was pretty much up to your PI/professor (and when I had the scholarship the professor didn't make a difference between scholarship holders and employees - he argued that this would only create more and unnecessary friction among people who substantially did comparable work).
However, there is a newish court decision that employers must properly document the working hours of all employees. Properly tracking working times of PhD students and postdocs will create huge difficulties with overhours. Whether anything will happen in practice is a totally different question.

From the "work a lot" aspect, you'd probably be fine as employee as well because if you have overhours, you are supposed to take them off as soon as possible. This includes taking days of during the week. What is more difficult is that your employer may not be allowed to let you work the times you do now (long hours, evenings and  Sundays may be problematic) 


pension cass contributions are mandatory for employees. However, if you do not reach the required minimum of 5 years of contributions, you cannot get a pension and instead you can get the employee half of the contributions paid out as a lump sum. If you have more than 5 years of contributions, you will be eligible for the corresponding pension payment once you reach pension age. Regardless of where you are (within the EU, "your" pension cass will also pay out the German part)
As an employed post doc, academic freedom does not apply to you: you are bound to the directions of your employer.
Many academic PIs let their postdocs do their own research, but some PIs or institute directors like to excercise their power... 
In Germany, a fixed term contract can not be canceled by either party once the probation period (6 months) is over. (An agreement where both sides agree to void the contract is always possible, though.) The employee has the right that the employer agrees to void the contract, though, if they have a better offer. But they need to actually have such a better offer. 




* there is some concern that since the pension cass will receive mandatory contributions if they find it to be an employment contract they are not exactly unbiased in these decisions in general (that's not only about scholarships, also about other contracts such as freelancing).