I have both ,use my 15.5"laptop only when traveling and it is convenient, however the laptop is slower and the desktop has better expandability for more storage.

If it's on your lap you do feel the heat although the newer ones may be better.

I prefer the full size keyboard of the desktop and recommend an optical mouse if you get a laptop as the touch pads to me are kind of "klunky" when working in BIAB/RB.

If you have or are getting a big screen tv I would recommend a 1080 HD LED which can also be hooked up to either type of computer and give you excellent resolution... if you can set up a desktop nearby or get a long connector.
Really makes up for the laptops small screen size!

There are several comparison sites like this to help you decide:

http://www.pcworld.idg.com.au/article/360605/buying_guide_desktop_pc_vs_laptop/

Both will do the job, just depends on you needs and price range.
Best wishes,
Carkins