lammert - 11:40 pm on Jun 12, 2010 (gmt 0)
Hi Paul, first of all Welcome to WebmasterWorld!
Your decision which server to upgrade to depends on the problems you have with your current server. A slow response can have several reasons. If your sites use a lot of database interaction, your disk could be too slow. The disk may also be running out of space which causes fragmentation of new files and a lot of seek actions to read in information from the disk.
With a script heavy site, it may be the processor which is slowing down the response. In that case the move to a multiple core server will help.
Another bottleneck can be your RAM. 2GB may be not enough to contain all your currently running processes. If the server runs out of RAM it will start to swap portions of temporarily unused memory to disk, which causes increased disk traffic and delays when those memory blocks are needed in RAM again.
To check which problem is currently slowing down your server you need shell access to the server to run some diagnostic utilities. Do you have SSH access to this server?