Well I have a Finalizer. John's correct- they are completely different machines.
The finalizer is basically a collection of mastering tools- EQ's, multi-band limiters and compressors, very precise level setting tools, and some "fairy dust" toys. Also sample rate conversions and high quality convertors for digitizing audio masters. The whole thing is set up to give you a lot of control- it does many different jobs.
The Aphex, by comparison, is a one trick pony. With very few controls or options it tries to emulate a general "big sound" that home enigineers generally don't get in their own. It's not very versatile, but it fine if its all you're looking for.
If you're looking for a tool to start getting a sense of what mastering is then of your two choices I would definately go with the Finalizer. (I should say that I don't mean
the Finalizer Express. I don't know anything about that unit, though I would guess its more usefull than the Aphex.)
If you're new to mixing, however, I would look outside of your choices... and wait. Its *REALLY* important to learn to mix first before getting into mastering tools. You'll just slow down your mixing learning curve if you're trying to fix things at the mastering stage. Playing around with mastering is a good way to figure out what needs to be fixed in your mix... but then I'd go back and actually fix it in your mix since you can.
Take care,
Chris