I want to use DTA, but on my website I have an Express Server version. Can I backup my DB on Express server, restore it on my personal computer with Enterprise Version, make some tuning by DTA and then restore it back on webserver Express MS SQL? Are they compatible? Both MS SQL 2008 R2, but one is Express and second not.
As long as you don't enable any features that aren't supported on Express Edition, you should be fine. For example I think you can use DTA to recommend table partitioning which obviously won't work on Express edition. The other thing to think about is that the server running Enterprise Edition might have a lot more memory or CPUs, so the optimizer on that server might make much different plan choices than it will on your web server.