Depending on what you're doing, a 3.2+ GHz dual core could work better than a 2.4 GHz quad core. If you're not really comparing benchmarks... the most perceivable difference in games, for example, comes from a GPU upgrade. A couple FPS on a benchmark really isn't something you'd notice.
More memory keeps things from paging to the hard drive... which is a big cause of a 'feeling slow' PC. Just being generally 'modern' keeps things reasonably fast. You might not be able to run very high settings on the newest games... but it'll get out of its own way. Since you had the old system, and have the new upgrade... you can tell how its improved.