I am trying to decide on a future path for myself. I currently work in the digital technology field and enjoy researching and learning new concepts to keep up to date, especially in the machine learning/data analytics fields. My company will pay for a Masters degree for me or if I petition and get approval from the executive level a PhD. I would also like to move in that direction with my career. I currently have an MBA and MS in CIS (Boston University). I would really like to be able to teach at a university in the future though, I expect it will still be at least 15-20 years down the road. In the mean-time I would be interested in being able to teach in an online classroom perhaps just one class to get the experience. Would anyone have a suggestion on whether I should push to get the PhD or would I be better off getting another MS in Computer Science (Machine Learning) from a school such as Columbia University?
Why would you want a 3rd master's degree?! Of course, unless you're not really cut out for a Ph.D. Master's degrees can only get you so far in higher ed teaching.
In your case, I would recommend a Ph.D degree since you like to teach and research. There is no reason to get a third master degree since you already have an MBA and a Master in CIS.
What is your undergrad in? Do you have the appropriate background for master's level work in computer science? That has not been made clear. I would make sure you are familiar with the prerequisites on Columbia's requirements page, as they may require you to take courses to satisfy prerequisites if not already met. That said, you have to ask yourself, what you are most interested? If you are more interested in machine learning or data analytics, I would encourage you to go for a master's in either. Computer Science inherently will be more valuable as well as more challenging. It sounds like right now and for the next 15-20 years, you will be a practitioner, so these are things that you can use to strengthen your career. Your interest now is not in becoming a faculty any time in the near future. You could go for a terminal degree, but a lot of that is research for your dissertation, which may not be directly applicable to your current career. You could also try to find a terminal degree that would include master's level course work in data analytics or machine learning. I would recognize also that if you want to teach full-time somewhere above a community college level, you will want to get a doctorate. You could become an instructor or lecturer with just a master's, but the pay would be more limited. You may not care about that. If you do care and want to be a professor, you would need to recognize you would have to eventually get the Ph.D. There is also the ability to become a non-tenure track professor of practice with significant work experience and master's course work, so just having master's would not necessarily need to deter you. Colubmia is an Ivy League school, and if you have the academic qualifications, I would personally go for that in your situation. The degree from Columbia would carry more weight in the workforce than a Ph.D. from either of the schools you mentioned. But, again, be mindful of above mentioned considerations if you are interested in becoming faculty.
Since your company is paying, have you considered Stanford's online masters in computer science? I do not know their admission rate for their online program. Incidentally, for brick-and-mortar computer science programs, it is much easier to get into Columbia University than GA Tech, UIUC, etc. Yale and Columbia University are popular among international students and others who have the money and were rejected from GA Tech and other top computer science departments.
