I purchased cataclysm today, retail disk box. I was wondering, should I spend the time installing all of my game disks or download the client through WoW servers? I have a fairly stable broadband connection. I have a 4x disc tray i believe. Any thoughts?

disks. probably. maybe. why don't you test it and get back to us?

Depends on what your speed is, but unless your internet is extremely fast I doubt it will outpace the disc install.
 
You'll still have to download an assload of patches though.

You're probably better off installing the discs. You would have to download about  20GB of data if you go the download route (as I did). You can play and download at the same time though.

I DLed WoW quite recently and it was ready to play inside 45 minutes (while continuing to download in the background during gameplay).  I would say that's competitive with discs if you're installing the expansions.

Go for the download.
They got this thing called the streaming downloader nowadays.
It'll load your character's starting area for example and some zones around it first, then you can play and while you play it downloads all of the game that's left.
 
Way faster then spending days installing it like before.

If you just started playing, go with the discs.  If you just bought Cataclysm and have patched everything up until this point, download it.

If your connections half decent just dl, the streaming thing it does ensures you'll be playing within 30 mins of the initial dl and it will just dl data as and when it needs it. Sure load times wont be optimal but I found it to work flawlessly on my rather crappy connection.

Discs? The WotLK dvd allowed you to install the whole game from it, not just the expansion. I imagine it would be the same with Cataclysm.

" I'd go disc, because even if you download it, you still have to install it, so using the discs cuts out that first step. "

" @TaliciaDragonsong said:

" @gakon5:  Might be, I put in my WotLK discs, installed that and right after I got the streaming tool. "

Yeah, but the OP is asking about the merits of installing the clients from the disc or just downloading them.  I'm saying you can't stream the clients, only patches; that's all. "  

The patching process takes forever so discs if you have cata.

I'd suggest downloading. If you install from any of the discs before Cata, you'll have to download patch 4.0.3, which I don't think is on the Cata disc and is 15 gigs of data (that simply replaces most of the vanilla data.) I could be wrong about that, but everything I've seen leads me to believe otherwise.

" The patching process takes forever so discs if you have cata. "

do. not. install. using the discs. 
 
I have installed wow both ways (disc and internets) and i can say without a doubt downloading the client is much, much faster. Not only do you download the up to date version of the game you can also start playing in 15 min, while it downloads the rest of game in the background.  
 
Expect a full day of installing and updating if you use the discs.