With so many linux distrobutions and desktop enviroments this is a question I get asked all the time or even if one version is better then another. What it really comes down to is
1. The intended use
If the reason you want to install linux is to setup a server, then you probably do not have a need for a gui as it uses more resources, conversely if you want to use it as an everyday desktop then you will want one. So in finding which is the best desktop its best to decide on what you want from linux.
2. The intended user
If the user that you’re installing linux for or even if you yourself a new to linux then you want something simple to install, easy to use and simple to maintain. Choosing a linux distrobution or desktop enviroment can come down to personal preference. There is no point installing something that you or someone your installing linux for will end up getting frustrated trying to do the basic tasks.
3. The hardware it is being installed on
Keep in mind that your six year old computer that has been sitting in the garage collecting dust might be able to run almost any distrobution it might not be capable of running some of the heavier desktop enviroments, if its old enough certain distrobutions might not be installable , ie the latest ubuntu will not install on my old laptop with a Pentium M processor as the cpu doesn’t support PAE which is required by the latest ubuntu and it derivatives.
To be honest that is oversimplifying it, there is more then just those three things to consider but in my opinion the most important and at the very least a good place to start. Do your homework on what each distrobution and desktop offers. Keep in mind that the first one you try might not be best linux operating system for you.