In my experience, the 2000 and/or 2100 mAh pretty much gives you an extra 10%-15% battery life at the end of the day...it's almost nothing, man. Others love it, but I honestly think that's more to do with the fact that it also adds barely any size or heft to the phone whatsoever. I went the other direction with it ; I got the 3500mAh from Amazon, which adds a ton of heft - both size and weight. But I absolutely love it. You may be more like the others and will wanna go for the 2100, since you care about the size of your phone - so I'd probably recommend that one to you. But I would also warn that you probably won't notice an improvement in your battery life - if you do, it'll be very minimal. I wish there were an in-between, something like a 2700 maybe? lol... something that wasn't over-the-top giant but still gave enough power boost to actually make a difference.
By the way, if you're worried about cost - I spent exactly (looking at the Amazon order right now) $18.23 and got a 3500mAh extended battery, with NFC, from a brand I didn't recognize. I took the risk because it was so cheap, I figured if it didn't work it wouldn't be a huge loss, and I'd just get the SEIDIO. Well, lo and behold, there was no need to go for Seidio (as much as I love their cases!) at all...I bought it July 23rd, 2012 and have used it ever since. It works flawlessly, and the battery life has been absolutely incredible. The brand is called "Onite". Here's a link:
Amazon.com: Onite 3500mAh Li-ion Battery for Samsung Google Galaxy Nexus I9250 (Sprint), Samsung Google Nexus 3, Samsung Galaxy X ,Battery With NFC & Back Cover: Cell Phones & Accessories
The price seems to have slightly increased to $22 right now, unfortunately - but that's still way cheaper than Seido's pricing on its 3600mAh battery.
edited to add: Yeah I don't know why the title of the item (and the corresponding URL link) is so varied and confusing, either. It even mentions Sprint in there. Onite has several listings on Amazon - although when I checked my order history, it takes me to that one, and I'm very sure the title was not all of that when I bought it. It works 100% perfectly fine in my Play Store, GSM, Galaxy Nexus. Whether it works in anything else; sorry, no idea. Just wanted to add this in here.
Hope someone can find this useful. I will definitely be buying another Onite in the future, if the price stays in this range!