I would not agree with baccusboy here. I have no problem whatsoever with copying files on Windows 7 x64. I would suggest that memory might have something to do with it. If you have less than 2 GB of memory, then perhaps 64-bit is not for you. Memory is cheap on the other hand. If your motherboard allows it, add memory and you will see noticeable improvement in performance (i.e. how fast files are copied). Of course, the 32-bit version cannot use more than 3 GB or so, so if you plan to have more than that (i.e. 4, 6, 8 GB or more), then 64-bit is your only choice.
I respect your opinion on the issue. I am running 4gb (2x2) of G-skill with 7-7-7-21 timings, but unfortunately, I am not alone in my feelings about copying files (in my case, more than one file at once to an external HDD):
Slow usb 2.0 transfer rate - drivers - windows-7
Read down into the thread, and you'll see a variety of complaints about the retail version, as well. Seems to be a Win7 thing.
Incidentally, this page would be most useful for the OP, as times comparing a variety of operating systems completing a variety of tasks are noted and graphed. Sadly, XP is not on the list, but Vista, Win7 32-bit, and Win7 64 are. Unfortunately, these charts are pre-release of Win7, but they are still good to see, assuming you're just deciding between 32 or 64 bit:
http://www.tuxradar.com/content/benchmarked-ubuntu-vs-vista-vs-windows-7
I might also add that, as much as people have bashed Vista (and rightly so, early on, IMHO) I wouldn't feel bad at all about having it on a computer today. I've been having some freezing issues with Windows 7 in the past few months, and I have to admit, I sometimes wish my machine were as smooth as my wife's Vista 64 machine. All was awesome with Win7 for the first few months, but something happened to start causing me problems -- be it an update, driver problem, or whatever. That, however, is a whole nother thread.
And one note to Kucing's post above mine... 32-bit will allow 4gb to install, but can only address/use 3gb of that. So yeah, you're wasting a gig of Ram. If you're someone who just does basic web surfing/office tasks, then 2gb is really all you need, in my opinion. With my 64-bit Win7 machine, when I was testing ram sticks to determine what my freezing problem might be, I was pleasantly surprised to learn that 2gb of Ram was more than enough for the general tasks that I like to do. I watched, and was using around 54% of my Ram when I had 2gb installed. Now, if I were a gamer, or into photo editing, It'd have to be 4gb or above for sure.
Lastly, a note to the 2nd post in this thread, from Bare Foot Kid. An interesting link was provided that says something like "64-bit, more benefits than just Ram." That article would be correct, but keep in mind -- it's from 2007. Here we are at 2010, and people are still waiting to see much of a difference. I think that's pretty telling!
Mostly, it comes down to what you want to do with it. I'd go 64-bit, merely because it's more future-proof, but if your machine is older, or just a web surfer/office type, then do whatever you want.