There are pros and cons either way. :-)
Max RAM Blizzard: 128 MB, 256 MB w/SCSI kit
Apollo: 32 MB in desktop, 64 MB in tower config
Apollo has crap (non-DMA) SCSI interface, Blizzard SCSI is much better.
Apollo has much faster custom chip access, and is probably better suited for AGA demos - only downside are the (very) few demos which require over 32 MB (in which case you can simply leave the case open while watching Starstruck). Another benefit to the Apollo's faster chipset access - 5.1 MB/s raw read with Jens' IDE-FIX Express, vs around 2 MB/sec with the Blizz.
Apollo's FSB can be set to 1/2 CPU clock. This means rates over 80 MHz (possibly a bit more) are easily reached with a Rev 6 68060. The Blizzard is always 1:1 CPU/FSB, expect a maximum overclock of around 70 MHz, and the SCSI card may crap out when overclocked.
Blizzard has the option to use Piru's excellent BlizKick program. (Though some modules can be converted for use with RemApollo.)
I've owned both, and both are outstanding. I doubt you'd be unhappy with either. There would be an enormous boost over your current card. I'm very happy with my Apollo, since my A1200 exists only for demos, and AmiNetRadio while I surf on the PC. :-)
Bottom line:
If you're not going to overclock, want a nice stable card for general use with an excellent SCSI option, lots of RAM, go for the Blizzard.
If you want to watch demos, overclock, do CPU intensive tasks (like AmiNetRadio) shoot for the Apollo.