Very subjective. I'm going to use the Apple //e Platinum as the comparison point, as it was the last true Apple II line, since the GS is really next gen.
Graphics - Commodore 64 wins hands down.
Sound - Commodore 64 wins again, but if you want to include the Mockingboard, it definitely becomes closer.
Price - Commodore was the king of cheap.
Durability - Likewise they were built cheap, the Apple is much more durable.
Expandability - Apple II line has internal expansion slots, so the edge goes here, although you could probably do similar expansions on the C64 with external peripherals.
Performance - Tie
BASIC Programming - AppleSoft BASIC is better than the Commodore BASIC on the 64. Just easier to use, especially to create graphics and access the DOS.
Gaming Library - C64 has more advanced games due to Graphics and Sound mentioned above.
Business Library - Apple II has 80-col support, most business software supported it, CP/M on Apple was good, bad on C64, so Apple wins.
Keyboard - Apple, no doubt, the C64 has one of the worst non-chiclet keyboards ever made.
Open-Architecture - Tie
Design / Appearance - Super subjective, but I prefer the Apple because the Computer, Drives, Monitors can all be stacked into a clean setup. The C64, has wires coming out the back and side, you really need a large desk or a special stand to allow the monitor/drives to live above the C64, otherwise it needs to be off to the side.
Overall, I prefer the Apple II, it's just a bit more fun to collect for, and if I were to be using one for any serious applications back in the day, the Apple would have won out. The C64 is definitely more of a gaming machine, and if I wanted it as a game console I would have gotten a C64. Although to be honest, if I just wanted games I would have picked an NES!