The biggest differences between these applications lie mostly in setup, flexibility, and other included functions.
LapLink and pcAnywhere are the two programs with the most features, including file transfer, voice chat, shared clipboards, the ability to reboot the host computer, and a plethora of connection options (modem, direct cable, network, and Internet). They work the same way: run the program on the host computer, then run the program on the remote computer to connect.
Both programs also have security features such as encryption, customizable file-sharing rights, and keyboard and mouse locking. LapLink, the Methuselah of the group (it started life 15 years ago as a DOS file-transfer utility) comes out on top by also including a synchronizing utility, printer redirection, and the ability to connect to or from a computer that isn't running LapLink.
LapLink has a pretty good balance between features and ease of setup. Although configuration can be a little tedious, the various options are very straightforward. The manual is clearly written and diagrammed, though it doesn't tell you how to turn off the omnipresent online help (the big question mark on the toolbar kills the automatic popups).
In comparison, pcAnywhere lags a little in features and ease of setup -- there are just a few more hoops to jump through, and the manual isn't quite as user-friendly -- but is otherwise almost identical in practical terms. (Even in its flaws: although you can customize the bit depth of the host desktop image to speed up screen updates, the image isn't antialiased -- making some of the text hard to read if the window isn't full-screen.) pcAnywhere's biggest advantage is its pricing scheme for one-time jobs: a 30-day license can be had for peanuts (and fully refundable peanuts, at that -- if you later decide to upgrade to the full package, you get the cost of the 30-day license back).
If you're just looking for remote control and don't need the other bells and whistles, you might consider Windows XP's Remote Desktop. Although it's free (it's part of XP Professional, though the remote computer only needs Terminal Services installed, available in any post-Windows 95 Microsoft operating system), there is a price to pay: setup requires you to be familiar with setting up Web services. If you're not, the convoluted online help makes you long for the old days of tree-killing paper manuals.