Should I do an MBBS before/after taking a doctoral program in neuroscience? My goal is to become a professor in neuroscience. At the moment I have a master's degree in computer science. During my studies, I did research in neuroscience but from a computational aspect. I succeeded in publishing two papers during the program. I am mostly interested in clinical neuroscience. Therefore, there are two questions I would need an answer to:


Does the degree MBBS (Bachelor of Medicine, Bachelor of Surgery) allow me work as a doctor? Treat patients? And, most importantly, run clinical studies as the person in charge?
Should I get the medical degree before or after doing a science PhD?


It seems there are some PhD/MD programs (I don't understand the difference between MD and MBBS) but they would take +9 years in most places. Doing a PhD and medical degree separately seems to be a faster route (3 year PhD and 4 year MBBS, if this MBBS is sufficient).

I would really appreciate any help, there's a huge amount of variation in information I can find from the web.
The distinction between an MD and MBBS is the US versus the British system of medical training. Both allow you to practice medicine in countries that support each system. Confusingly, it appears the MD degree in the UK is also a post-MBBS research degree most similar to the US PhD, though you must have already obtained an MBBS to train for an MD (source: Wikipedia).

A quick google scholar search for MBBS reveals many published clinical trial studies where authors have MBBS degrees. For example, 

Article 1 - Article 2 - Article 3 (in Lancet)

So the answer to your first question is yes. Perhaps the only thing to consider is where you ultimately want to practice. Ideally, you'll want to do your training in the same country. There are lots of crappy things about training in one country then moving to another--mainly, many places will make you retake the country-specific licensing boards. 

I'm a little skeptical of your proposed number of years of training. In the UK (where MBBS originates), training is 5 to 6 years in length, generally two years pre-clinical followed by 3-4 practicing in the hospital. As for the PhD, Europe and the US have different expectations. I encourage you to check out this concise comparison from a different post. Essentially.. time to get a PhD is often fixed in Europe, while more open ended here in the US. But, as is emphasized above, training should be about learning the key skills necessary to succeed in academia, which is your stated objective.

In regard to which to obtain first.. I would argue for a PhD followed by medical training. Clinical skills are easily forgotten. I recommend once you've done medical training, it's best to start your clinical/research practice. This is especially important in any country with regular maintenance of licensure exams. This would be much harder if you primarily did your PhD rather than practice medicine in the intervening years. 

The truly best order though is probably what is done in MD/PhD programs in the US. It is widely considered optimal to observe the following order (US medical system): 2 years didactic training (medical school), entire PhD (3-5 years), second two years of clinical training (medical school). 

The reasoning behind this order is that the first two years of medical school are essentially pathology and basic science classes that will give you a broad introduction to how a body works at a gross and microscopic level. This will give you a biomedical background that no PhD student gets. You also won't use 99% of what you learn in the lab... but in principle, you might draw connections outside your own field that others would have no background to make.

PhD training is much more focused on a particular field, with the emphasis being depth rather than breadth. In your PhD years, you will master a remote niche of science, hopefully while learning how to be a good scientist, how to write, and how to obtain funding for your ideas. 

Empowered by this, you then return to the clinic, where you realize most everything we do in medicine is empirical! Ideally going through the clinic you think about all the biomedical questions for which we have no answer. After graduating, you continue on in residency training. In the US, there are research-oriented residency programs that cut out a year or two of training in place of pseudo-postdoctoral research fellowships.

The length at most US MD/PhD programs is 8 to 9 years, which is definitely faster than obtaining an MD and PhD separately in the United States. The main reason is that the cross-training allows some MD courses to count towards the PhD, and because lab rotations are done in the summers before the first MD year, and between the first and second, when normal MD students are free to do what they like.