Generally, a desktop will have more processing power than the average laptop. With a desktop, you can specify components down to the triffling little details while most laptops will not allow you much in the way of options.
With a desktop, you can specify motherboard, CPU, GPU, RAM, hard drive(s), optical drive (CD, DVD, BluRay, etc..), case, monitor, and so on. With a laptop, you get whatever components the maker decides to make available. Sometimes, you can change things, but most often, your options are severely limited.
It will really boil down to what you personally want to do with the system. Do you want something you can sit at home at your desk and surf the web, email, write letters, spreadsheets and the like? Or do you want something portable? While it IS true that you can buy a high end, high powered laptop (ala Alienware) that's got decent horsepower, you're also going to pay a premium price.
Either way you go, check the applications you want to run and see if they will work under Win 7 64 bit without issues. You're going to find that Windows 7 is the operating system of choice and more often than not, it's going to be the 64 bit flavor. Given you want to run multiple apps at once, I'd go with more RAM.
I'd also opt for a decent GPU (video chipset). My video card isn't state of the art, by any stretch (Nvidia GT 220) but it has 1 GB of dedicated video memory (a feature lacking in MOST laptop configurations). I can run a lot of graphical apps in multiple windows and tabs without too much grief while many of my friends with laptops have a really hard time with the same task in only ONE window. The GPU is becoming more and more important, almost as important as CPU and RAM.