Syndicate wasn't an AGA game so won't need a lot of memory. Compare 512KB of an A500 to 2,048KB of an A1200 and I'd say there's something else at fault.
I couldn't get Syndicate to work on my Blizzard 1230-IV 50Mhz - it was always too fast and would crash at random intervals. Needless to say it's even worse on Blizzard 1260.
While we're on the subject of Syndicate, even though the Atari Jaguar version has more colours and runs on the same 68000 processor (albeit with 2x super chips helping it out) the A500 one is actually better! The Amiga one has animated interludes and intro, a pulsing noise in the background, smoother scrolling and crisper sound samples.
Also, did you know that by pressing `D' on the keyboard you can self destruct?
:-D