Because this new server is dedicated I think it will do great in comparison, even to the dual xeons (I hope). My question is how and where will the 4 times the cache size on my xeon help out - or where would it be most noticeable or most useful? This box is for everything, mail, http, database, etc....
Its really only 2x the cache, as the old server has two cpus each with 1mb cache. However the new single cpu dual core 3060 is a good amount faster than the older dual cpu single core xeon 2.8ghz setups.
Based on a lot of MySQL benchmarks, it seems the added cache can be a big advantage there.
Overall, the dedicated system you have now should perform better than the shared system you were on before. With the move from shared to dedicated, that box should EASILY be enough for you, likely for a good long time as well.