At this point, besides exterior design, there is no difference between the G series Logitech and the Razer Copperheads. Both use the exact same 2000 dpi UV laser hardware. One advantage of the G5 is that it is a great shape for a right handed gamer. I'm a lefty, but I don't let that stop me from enjoying a good thing for what it is. The G5 also has weights inside so you can customize the center of mass of the mouse to your personal preference. Nifty, but really not a big deal unless you are running on a low friction surface with teflon feet.
The Razer has a couple advantages, namely better drivers and onboard memory. It is also the only mouse that currently takes advantage of full USB 2.0 sampling speed rates, meaning that it uses all of the bandwidth of USB 2.0 to transfer information, providing a little better sensitivity. The On-The-Fly adjustment of the Razers is better, as well. Needless to say, I have a Razer, and with the Pro Tools kit, you have the adjustable weights there as well.
There is a couple other contenders, as well. First of all, Microsoft does make a 1600dpi laser gaming mouse, although due to the lack of previous participation of M$, there has not been a lot of interest. Creative also makes the Fatal1ty series of mice, proving yet again that being good at gaming doesn't make you great at engineering. It looks pretty horrible, but the hardware must at least compare well with the specs of the G5 and Copperheads.
If I was looking for a low cost mouse, I would go with either the Razer Krait ($40
http://www.razerzone.com or the MX518. Best price I've seen on Logitech is
http://www.justdeals.com although I carry the Razers, Logitechs, and Creatives on my site as well.
The gaming mouse debate has been going on a long time, I've been in the midst of a lot of it since I brought over one of the first 100 Razers to the US from Singapore.
One thing you are really going to have to ask yourself is what is your primary function for the mouse (FPS, RPG, RTS) and what price range do you want? For FPS, do you want steady or twitchy, or both? For RPG, does it really matter? For RTS, you'll want decent sensitivity but with a smooth polling rate. For the money, Krait, MX518, or the cheaper Creative would be a great start. Let us know what you pick, I'd love to hear about it.