The question is interesting in relation to the current bias against four year degrees for software developers in some circles. If, as Peter Thiel claims, you don't need a degree, then it shouldn't matter what your degree is if you get one. So, from that perspective, a tech degree or a liberal arts degree shouldn't make a difference. If a liberal arts degree makes for a more intellectually well rounded person, then it could be argued that that's the better degree for tech.
Of course, I don't buy Peter's argument at all. A good CS degree teaches foundational methods that can be applied throughout a career. Don't get me started on the number of times basic complexity theory or knowledge of the full memory hierarchy has helped improve performance of web pages. Most hobbyists don't have those skills and write them off as just academic oddities. A good CS degree also exposes you to a range of technologies and methods for developing software (no, CS is not just math, no more than physics is just theoretical physics). It gives you an environment where you can develop your skills and gain exposure to the breadth of topics in the field. It's a Good Thing(tm).
Should all programmers have CS degrees? Of course not, but those that do are always going to have an edge over most of the other ones (there are always exceptions - I know a few great developers without degrees).