This is one of those questions where you will get as many opinions as you get respondents.
As far as I am concerned there is no competition i.e. a desktop wins everytime. Why? Because laptops are primarily made for people on the move or those that are pushed for space and therefore are a compromise. They will do everything a desktop will do but generally more slowly. The big drawback is when things go wrong outside of the warranty when you can expect horrendous repair bills that is if you can get it rapaired at all. They are usually propretory which means that they use non standard parts. On the plus side they now generally cost less than a desktop and use less electricity and you can take them on holiday.
With todays laptops you can plug just about anything into them the same as you would a desktop but beware of netbooks as they are specifically designed for basic tasks such as surfing the web and simple word processing etc, have slow processors and dont even think of playing games on one.
In my opinion there is no competition, its a desktop every time but then I would say that as I build my own and yes I have several laptops but dont do any serious work on them.
No doubt others will disagree.