Well that's a good question, I guess you "could" have been a professional basketball player. I don't think there is a rule of thump to use only "would" and it isn't excruciating to my ears (at least to mine) but personally for some odd reason which can't really explain I would use "would". Maybe it's because (I think) "would" is more definite than "could", and therefore you risk making it a suggestion.
Would is more definite than could, as KON and Loob said.
In answer to the original question I would always use "could" because it´s something that seems to be being given as an opinion more than a fact. "Would" really implies that this is absolutely going to be the case, that when this person becomes taller they will play basketball professionally. This isn´t really something you can know for definite, so it´s best to use "could".