It's also possible that other things are bogging down the older computer, such as crapware, malware, disk fragmentation, low disk space, etc. You might be able to speed it up by uninstalling all software that's not absolutely necessary (including browser plugins and toolbars), then running a thorough scan with MalwareBytes' AntiMalware and defragmenting the hard drive.
You might also want to review the antivirus software you're running on both computers. McAfee antivirus is notorious for slowing down PCs, and many other antivirus programs drag down performance with their on-access scanning. A recent benchmark rated Microsoft Security Essentials #1 in terms of detection and low resource usage. I've also noticed that Avast! antivirus doesn't bog down the system as much as other antivirus apps I've tried.
Doing a clean reinstall would also probably help, but first I'd recommend booting both computers from an Ubuntu Linux LiveCD and seeing how they differ in performance when they're both baselined. This should give you a better idea of whether a reinstall will bring the slower computer closer to the faster one in terms of performance, or if the performance improvement is likely to be negligible. Since this is just a quick experiment and these are both older computers, you might want to try an older distribution of Ubuntu first, because the newer ones are a lot more resource-intensive.