What happens where I go to school is that the Game Programming degree will really put your foot solidly in the door. We actually feed to a variety of studios, some cooler than others. Our Game Art degree is a little less great because that is a job that requires a strong portfolio. Being trained and having a degree helps, but ultimately your artwork is what gets your jobs. My school claims that the average salary for people with the programming degree is 70 000 USD which seems slightly unlikely to me having worked as QA and later on as Designer. That said, I got paid a decent amount for it being my first industry job and not being done with my degree yet.