Both are fantastic companies that I loved, especially during the 8-bit and 16-bit eras.
It's a hard choice, but if I had to choose, it would be Capcom. There's the obvious reasons like the long-running Mega Man and MMX series, Resident Evil series, Street Fighter & SF Alpha series, and the VS. series. But there's also a lot of great lesser talked about games/series like Bionic Commando, Duck Tales 1 & 2, Knights of the Round, X-Men: Mutant Apocalypse, and the Breath of Fire games among others.
That's not to say Konami is bad by any means, though. TMNT games, Gradius games, X-Men Arcade, Metal Gear Solid, Castlevania (this series alone almost makes me want to change my mind), Sunset Riders, etc.