Architecturally the systems are very different, and the use of SPUs allows Sony to claim more "operations per second" because of the ancillary processors--which is where all the "more powerful" hype comes from.
However, the simplified explanation is that the PS3 has a single-core PowerPC processor with a series of special ancillary processors that are super-fast at what they're good at, but aren't general purpose CPUs. The 360 has a triple-core PowerPC processor that doesn't offer as many raw calculations per second, but you can't compare SPU operations with CPU operations. It's much easier to program for, as each core can work on any kind of operation.
The 360 has 512MB of memory and an additional small amount of frame buffer memory; the PS3 has only 256MB of memory but it has 256MB of graphics memory.
I think in the end, the technology is a wash, because writing a game to really take advantage of the PS3's SPUs means heavy recoding to do a version for PC or 360. So I'd imagine most multiplatform games will never take full advantage of the full bank of SPUs -- they'll be used for stuff like fast graphics libraries.
What this boils down to is two very different architectures that have strengths in different areas. In the end, both consoles can fill an HD screen with beautiful imagery.
The radically different architectures are going to make multi-platform game quality interesting. Will games just be programmed to a baseline of common capabilities, or will they be optimized for one platform and then get mediocre ports for the other?
So it's going to be more about (1) the console experience -- is the mature Live service what you want, or are you willing to sacrifice that refinement in exchange for "free?" Do you like friends lists and achievements, or is the ability to play your PS1/2 library a sell point? (2) Which console has the games you want, and (3) do the non-game capabilities matter? Linux, XNA, HD movies, etc?[/b]