I just did a search on all three sites for "2x2 yellow brick."
Peeron returned 50 results in a wall-of-text format with no images and I really didn't want to sift through it. But I did and none of them was a standard 2x2 yellow brick.
BrickLink returned 16 results, all with individual images of specific items, none of which was a plain yellow 2x2 (but almost all of them were 2x2 bricks colored yellow or green).
BrickOwl returned 58 results, most of which would make sense to someone who had no idea what Legos are, but none of which were a standard 2x2 yellow brick. More than half of them had a generic white 2x4 "this product is a Lego brick" image, which meant I had to read the description of each item to discover if it was what I was looking for.
So out of those three websites, BrickLink was the one that most-quickly informed me that I was using imprecise (but pretty good) search terms and Peeron was the one that most-quickly made me feel that I never want to look at that website ever again. BrickOwl made me feel like I was searching eBay for a replacement screw to the door panel on a 2003 Saturn Ion with the grey door panels instead of the standard black ones, and I know the original screw was a phillips head but I need a hex-head screw. I had to actually click on 47 results before realizing that "grey" isn't the correct color name and I needed to look up what Saturn called "grey" in 2003 (it's "Storm Gray," btw).
The problem with wanting a simple search function in the Lego catalog is that the catalog is so huge and the terminology so ambiguous (to the uninitiated) that a simple search query isn't likely to give you what you want unless you ARE familiar with the terminology or already know the part number you're looking for.
Conclusion: as complicated as BrickLink appears to the new user, it is the best-kept database of the three. There are images for (I'm very sure) every item, and the catalog is broken into very easy-to-understand categories. The website is difficult to navigate and the forum is absolutely useless, but if all you want to do is buy bricks, BrickLink is it.