I have checked the Epson.com website and found the support details for the free software from Epson for these scanners:
The older scanner (model 2450) is supported by Epson in both Windows 7 and Vista in 32-bit mode only. For 64-bit installs they suggest that users purchase Vuescan as the Epson drivers do not support this scanner in 64-bit mode.
The newer scanner (model 4870) is supported by Epson in Windows 7 and Vista in both 32-bit AND 64-bit mode. So you can use the Epson software with that scanner regardless of whether you have a 32-bit or 64 bit install.
Of course, Vuescan works really well with the newer scanner too...but if you don't want to purchase it you should have no problem using the 4870 with either of those Windows operating systems.