What do you think about a part time PhD vs full time PhD, when the part time PhD involves working on my master's thesis research full time?
I can relate to your situation somewhat. I have been full time while studying my Masters and now my PhD, but in my case, there were no direct links (the job pays the bills).  The final academic transcript says the degree, not whether you did it part or full time.

While working full time, I finished my part time Masters (physics) in 3 years and are on track to do the same with my PhD.

It really depends on how much time you can realistically spend on your research so that it does not impact on your paid job, your lifestyle, family and friends and such.  Whether it is worthwhile really depends on you and what you are aiming for - it sounds like it may well be worthwhile for you, given your job is in the same field and that you are aspiring to have a career in Academia.

Hope this helps.