I agree with mastrom101 and Eduello. Additionally, you need to assess how much you would use one over the other. If you travel a lot or just spend a lot of time out of the house and you need to have access to capability beyond email and websurfing, then a high-speed laptop might be your answer. Otherwise, you're going to get a lot more bang for your buck with a desktop, with a cheap laptop or tablet as your secondary.
The best match-ups, IMO, are a desktop and tablet, or a laptop and a good, large-screen smartphone. Or if you work on-the-go like I do, you can get all four and mix and match as the situation dictates
You might try setting up your own value comparison table. Use three columns, one each for desktop, laptop, and tablet. Then add rows listing, in order of your personal priorities, your computing requirements. Assign an arbitrary value to each requirement (e.g. top priority is worth 10 pts, second 9 pts, etc), then run down each column and check which requirements each platform meets. Whichever platform gets the highest total should be your primary and should get the lion's share of your budget. Then you can choose between 2nd and 3rd place for your secondary based on cost.
The table can be expanded to include as much detail as you want, and once you've decided on platform types, you can use the same technique to evaluate within the types. In other words, if you decide a laptop is going to be your primary, you can use a similar chart to help you decide which laptop will best suit your needs.