PhD with or without company partner What are advantages and drawbacks of starting a computer science PhD funded both by the university and a company, compared to a PhD fully funded by the university?

I can provide more details about the context pointing out some hypotheses that I have done so far.

A company:


will provide proprietary data;
will stimulate about solutions for current issues;
will impose constraints on PhD topic (it could be slightly modified, but no more); 
will impose some constraints about publications, e.g. they would delay publications until new outcomes are started in the company production line.


On the other hand, without a company:


no proprietary data;
less stimulating scenario compared to issues coming from a real scenario (?);
free management of PhD topic (you could modify significantly during the 3-year research);
no problem about publications;
more "theoretical" research.


I will appreciate any experiences, especially computer science area.
As I was observing this in Academia it works like "get as much clear funding as you can work out"? With a decent funding, you can diminish all stated problems; inversed move is much harder. That concerns from a side looked like you're already at a peak with a solid financial foundation and choosing from a huge amount of options. Maybe, the situation differs, but recheck the reality, just for sure.