The main difference is they stopped working on CS, whereas source they are continuing to work on. CS 1.6 is the last patch they came out with. If youre playing on source, chances are you won't like CS 1.6 - source was a major overhaul for CS. Mostly the only people who like playing 1.6 are the people who started playing CS before source. Anyone IMO who started playing post CSS release won't like 1.6 as much.
Try it out though, I love 1.6, it's great. When Source came out I bought it, and I didn't even play it, I stuck with 1.6 - there were many changes that a lot of people didn't like when it first came out, and I used to play in CAL so I didn't bother switching cuz my team was still on 1.6.