You don't absolutely have to have the same OS. Although it's true that having the exact same OS on the new server would be the safest way to go, as long as you aren't doing a System State restore of the OS.. and you've made your proper sacrifices to the Computer gods (ie, burn a 5 1/4" floppy at midnight while chanting "Bill is Great" ).. you should be able to get away with a different OS on the new server. As long as you aren't going backwards in versions, so to speak. So you want to match service packs, hot fixes and other patches as much as you can.
Plus, as the article says, you also want to match drive letters to the old server (although you don't have to match the sizes of the old drives, long as they are not smaller). That's because the configuration of your current Exchange server says "THIS drive\path is where I put my logs files, THIS drive\path is where I find my mailbox stores, THIS drive\path is where to find my Exchange program files", etc and so on. That's not stored on the server itself, it's in Active Directory. Thus when the new server becomes your Exchange server, it's going to ask AD, hey, where do I find this, that, and the other thing? The new server, since it's taking the old server's place, will be told to look in those same locations. So it'll have a nasty little hissy fit if it doesn't find things in just the right places.
If you've got the time and equipment, I would highly recommend creating a test environment and trying out the migration steps. Make yourself an isolated little test domain with a test Exchange server, etc. Matter of fact, if your test equipment has enough umph (drive space, ram, etc), you might even try doing a System State restore of one of your Domain controllers (one, of course, that has the Global Catalog) and and System State & file restore of your Exchange server in your test environment and then try the migration. It's amazing the little "gotcha's" you'll find when you are able to test the steps with stuff that's as close to the real thing as possible. Old programs that you thought weren't being used that still have junk leftover in your Services applet, drivers that don't work on the new OS, etc. etc. A test walk-through can be a life saver.