(1) Desktops have vastly better keyboards. So if you're actually going to do any typing, particularly if you do it properly rather than pecking with one or two fingers, desktop wins. Except of course that you can buy a separate keyboard and plug it into the laptop.
(2) Desktops have proper mice, laptops have little tits you have to push around or grotty touch pads. Except of course that you can buy a separate mouse and plug it into the laptop.
(3) Desktops have whatever screen you choose to buy. Laptops have whatever screen they come with. Except of course you can buy a separate screen and plug it into the laptop.
So ... if you buy a laptop and decide you can't get on with the keyboard or the tit or the screen you can buy external ones (I've got a real mouse for mine; put up with the built-in screen; choose not to use it for any non-trivial typing).
(4) Desktops are expandable much more than laptops - you can add memory, add peripherals, add disk, replace the graphics card, and so on. This is rather more difficult with laptops - typically you can add some memory, if you didn't get the maximum possible optional memory in the first place, but that's about it. Except that ... these days most of the extras you might want are available as USB plug-ins, so maybe not too much of a big deal here.
(5) IME laptop hard disks are somewhat on the slow side. Not a big deal maybe if you don't do disk-intensive stuff (I do, I'm a software developer).
(6) Only the brave go round upgrading or replacing their operating systems on laptops. Somehow this is a less scary experience on desktops - there's less worry that you won't be able to find and install whatever specialist drivers the laptop hardware needs.
(7) It is still the case that desktops give you more power for the same money, although the gap is no longer the factor of two that it used to be.
And the one thing in favour of laptops:
(8) Whilst it's not impossible to put a desktop in a suitcase and stick it in an aircraft's hold (I've done this in the days before laptops were commonplace) it's not much fun. Laptops are much more portable.
So, I have a desktop. I then decide whether I need a laptop as well ... and I've decided I do, so I've got one of each. But I don't think I could live with only a laptop.