Having read quite a bit of both, I have always regarded Vonnegut as more inspired by Heller than the other way around. I know Vonnegut published two novels before Catch-22(1961) appeared (at least in its entirety, he published just one before Catch-22 was serialized) but his style would not really come into shape until Cat's Cradle (1963) which immediately followed Catch-22 (Heller's first novel). Slaughterhouse Five (1969) would be six years later and has obvious similarities to Catch-22.
I maybe dead wrong and giving Heller too much credit here but that was always the impression that I got. One thing I know is they were friends. When Heller died, Vonnegut exclaimed
"Oh, God, how terrible. This is a calamity for American letters."
As for Heller's other stuff, I really like Picture This a lot. Heller's other novels were actually often good they just never lived up to Catch-22. Heller explained this when a reporter asked him why he hadn't written anything else that good. "Who has?", he replied. I think he was right.
And, of course, Heller had no element of Sci-fi. I think what I see similar in the two is irrelevant to genre. They both tore up chronology, treated the absurd as if it made perfect sense and wrote characters who felt powerless but were really had a good deal of control over their world.
