Can I have both? In life I mean. I can play guitar to a pretty high standard, I can write, I can act and have acted in amateur productions, I can draw reasonably well, and with a modicum of practice I could be much better than I am. Academically I'm capable of mathematics, science, arts and humanities. I'm versatile, but everything I put my mind to I can do to a high standard.
As to characters in games, I tend towards the same sort of character. Taking my ME character, she can not only snipe the wings of a fly, but she has a close combat speciality, and is proficient with hacking, negotiation (charm) and a single biotic power. All of these are maxed out traits, but they provide for a character who is versatile, but specialised in all of the versatile fields.