Depending on what type of work you are doing, I would say the computer hardware is fine, but your operating system / hard drive may need a good cleaning. The amount of RAM or memory is on the low side by today's standards, but everything else should be find for an average business computer.
I would take one computer and after backing up the hard drive, delete and re-install the operating system. If you are running Windows 98, then you should upgrade that to XP or Windows 2000. Then re-install your applications. 256MB may be enough memory, but I would plan on upgrading to 512MB for most and more for any power-users you may have if the computer will support it.
Doing a clean operating system will "defrag" the hard drive, and I suspect that a fragmented hard drive and OS that has accumulated a bunch of junk is what is causing you problems. As you are thinking, the machines you are considering buying are not much different except that they are "clean and fresh" and would be an "upgrade" only because they are new.