I've always seen A600 more like a budget version of A1200 rather than a new variant of A500: better graphics chip, IDE port, PCMCIA and new look-and-feel of the Workbench 2.04 (at the first sight hardly distinguishable from the Workbench 3.0) gave a taste of something new.
I feel that "budget A1200" is a misnomer. The IDE port was its strongest addition, but internally it's still just an A500 with ECS instead of OCS, and that never really panned out as leverage. Not even the additional 512KB of chipmem made a splash. No more than a handful of titles, productivity and games alike, took any advantage of it. Incomparable to the upgrade seen with AGA and a 14 MHz 020.
Sure, in terms of hardware, it was a slightly better A500, and you could plug it into better monitors than the A1080, and you could finally get "normal" IDE HDDs which were a fraction of the cost of SCSI HDDs with some expensive third party adapter.
But also, Kickstart/Workbench 2.0 was a million miles better than 1.3, and it opened access to a lot of very cool software. Even though the A1200 and A4000 got KS/WB 3.0, most new software remained compatible with 2.0, and only used 3.0's APIs for bonus functionality... the big leap was from 1.3 to 2.0
(of course, if you were purely game-brained, you'd probably be complaining that your A500+ or A600 didn't run KS1.3... bleh, you had enough RAM to softkick it if you wanted)
Indeed, it is a shame that the A600 didn't come with Kickstart/Workbench 3.x.
It had other improvements than just support for the AGA chipset's video modes.
"Datatypes" were pretty neat. Thanks to it, the Amiga got PNG support in all web browsers before many other platforms got it at all.