Well, that depends upon the application for a start, but I find I can run virtually everything I wish to quite comfortably (I've never really tried heavyweight games however)
I do keep an eye on apps though to see which ones are over-utilising the cpu when idle/in the background as too many apps doing so simultaneously can induce lag and stutter.
The one family of apps that do give me cause to desire a much faster cpu are browsers; Visiting java-rich sites or most forum sites is an exercise in patience so I advise tapatalk (a lot of forums aren't supported though) If you are going to do a lot of Web browsing I recommend Opera (full - not mini) as it is far more stable, it's smoother, and much more compliant than all the competition despite its large size.
On my 600mhz single core I had many issues before I rooted due to lack of memory also. Now that I am rooted and shuffling things off to sd ext partition my tablet is a much better, smoother, faster machine. I now have close to 150 apps installed and the only times I really long for a faster processor is when a program wants to read in the entire apps list. Oh, and at boot-up - which can take ten minutes before everything is loaded and my tablet is usable, but I only re-boot once a day usually.
Unless you're mostly a gamer I'm sure you will find a 600mhz to be fine, though of course if you can afford a faster phone/tablet you should probably do so. But most of all, I heartily recommend you root as soon as possible.
Good luck, Mike