As I noted above, performance is no contest ... the Core 2 Duo. Haven't noted a direct comparison of the latest mobile versions, but note that even the mid-line Core 2 Duo E6600 (which is clocked just a bit above the mobile version) beats EVERYTHING that AMD makes, including the FX62. And a Turion doesn't come close to the FX62.
For question #2: As sparkmaker noted, both CPU's support 64-bit operations. You can install either a 32-bit or a 64-bit OS on either.
Bottom line: Both are good processors; but if you're interested in the best performance get the Core 2 Duo.