There is a huge difference if you study part time at a private university while working full time and studying there full time.
In my comment below I explained in detail why a student from a private university with no work experience is less desirable for an employer than a counterpart from a public university.
But I also pointed out that this doesn’t apply to students who offer additional qualifications like years of work experience in a full time position. I got my Bachelor at a private university while working full time. The degree is an addition to my years of experience and seen as a plus by many employers. But the degree would have almost been worthless without this experience. Plus, I have met students who did the full time version of my degree and the issues I described below apply to 90% of them. There might be exceptions but if someone asks me „Will I be able to get a good job with an attractive employer if I study full time at a private university and don’t have any additional work experience“ the truthful answer is most likely not.