It all comes down whether you really need it's mobility, most of times (in my case oc) i'm at home playing with friends through voice chat, and seldomly have the need to game elsewhere...
Just as said above, you're probably dead set with a laptop if you choose it, with a full blown desktop you could always upgrade it... and if you really wish it to be mobile, you could always build yourself a small form factor PC... Just pick a mATX mobo, some tiny GPU and Case and there you go, as mobile as you could possibly get while keepin all the benefits from a desktop.