The age old question!
Both have advantages and both can be professional quality. Screen printing will be a bit higher quality, but will be a lot harder to start doing yourself and be color-limited (and heat transfer vice-versa). There are other methods too of course, such as plastisol transfers or vinyl/flock transfers - each with their own advantages.
Here are some threads where this topic was discussed in the past:
http://www.t-shirtforums.com/showthread.php?t=298 (Older thread, should still be relevant though)
http://www.t-shirtforums.com/showthread.php?t=5372 (Recent discussion)
Both have advantages and both can be professional quality. Screen printing will be a bit higher quality, but will be a lot harder to start doing yourself and be color-limited (and heat transfer vice-versa). There are other methods too of course, such as plastisol transfers or vinyl/flock transfers - each with their own advantages.
Here are some threads where this topic was discussed in the past:
http://www.t-shirtforums.com/showthread.php?t=298 (Older thread, should still be relevant though)
http://www.t-shirtforums.com/showthread.php?t=5372 (Recent discussion)