IMO you don't need a Mac to get a computer that runs more smoothly, unless a) You really like the Mac or b) You are setting up a professional standard studio.
If a) then I don't think that at the lower end of the price range, it will be as powerful as a PC built to personal specs.
If b) then I think you're looking at a whole new ball-game where you won't use the computer for anything other than audio and it will cost a great deal more than a PC with acceptable audio capabilities, but then, you probably won't care so much about what it costs, if you're buying for a pro investment.
Compared with the PC, a Mac will seem like a designer toy (except it's not, it's actually a very powerful tool) with it's ' jazzy, bubbly, user-friendly interface. But don't be fooled - they do slow down and they do fuck up and at least with a PC, you're more in control regarding how you set up the drives and maintain them. There are many more options for how the architecture can be set up, such as adding more hard drives at relatively low cost and configuring the whole system to keep system areas clean, etc.
I think Pro Tools is very well suited to the Mac and I've heard of less problems with this combination than I have with Pro Tools on the Windows platform but then, a PC does need more looking after and attending to, to get the best performance out of it.
It all depends on what you're most comfortable with. If you like to tinker, the Mac will be limiting. If you want hassle-free performance but more of a 'ride along with Mac' experience, then you'll be happier with the Mac.
Both perfectly great technologies, with different approaches. Both enjoyed by professionals and home enthusiasts, in equal measure.
Dell, I used to really like but I've heard quite a few bad things about them lately. From what I've heard, their customer service isn't quite what they'd like you to believe it is and in my estimation, the path to true PC/Windows performance is to build your own, with carefully hand selected parts.
Sounds like a pain but actually it's not an option the Mac offers (actually I think they do self-build kits, but it was just a rumour I read somewhere) but on the upside, it will work straight out of the box. You're basically paying extra for someone else (namely Macintosh) to select parts and tell you what's good for you - and for the most part, it is good.
On a tight budget I personally would avoid Dell because of the way they sell you what seems like a great package but often there is some form of in-built upgrade restriction, when it comes to sound cards, either by form factor or by having no extra slots on the board. This kind of defeats the open architecture philosophy of the PC. Unless you go for one of the more expensive DELL models which are totally open to expansion (a true PC IMHO!) but have sufficient specs to make you very happy anyway. They just cost more because (a little like the Mac) you're paying for the brand name and the customer service (except I have ny doubts it's actually as good as the Macintosh customer service) so it kinda begs you to ask: why bother?
If I were in a hurry and money was no object, I'd probably just buy a DELL because they do ooze quality (as PCs go) for the most part - or, as some will say - they used to. My only experience of DELL is that they are solid and robust and the parts should outlast cheaper far-east mass produced stuff... but that was a long time ago. You'll need to read some current user reviews as I can't say very much more than that. I wish I could help more, but that's about as much as I know.
Oh, and on the question of laptop or desktop? Well, only you can decide how much portability means to you - but, as a general rule, pound for pound/dollar for dollar, you'll get better performance for your money with a desktop because the bigger form factor carries much more powerful, yet cheaper parts. You can get extremely powerful laptops, of course, but they come at a hefty price for the minaturization. The real servicable workhorse really ought to be under the desk. My laptop is a luxury, not an necessity, but again, that depends on the user.
Best of luck
Dr. V