I used to have a pitcher water filter. First a Brita, then a PUR. Recently, we finally switched to a faucet filter, and I much prefer it.
First off, I have gone to great lengths to avoid beverages in plastic (we buy our milk in glass bottles), so it always seemed a shame to me to have my water, which is what I drink most often, sitting in plastic. Second, that darn pitcher took up a lot of counter real estate. Counter space is always in short supply in our kitchen so this was very much not appreciated. Third, the pitcher always looked gross, because I rarely washed it and it got splashed all the time, plus plastic always looks kind of dingy after a while.
The faucet filter does have a few drawbacks. You need to use two hands to operate it, unless you want to waste a lot of water. This was not a big deal, until I found myself carrying around a baby in one arm much of the time. So now we keep a very small glass pitcher with filtered water on the counter (it is much smaller than a pitcher filter) for those occasions when I only have one hand free. Also for when my husband is washing the dishes. The filter also sometimes can be in the way when you are using the sink (especially if your sink is also full of dishes, as mine usually is), but you can easily snap it off completely. This is what we do when we are doing the dishes.
I like how easy it is to switch the filter on and off. I like the little light that tells me when it's time to replace the filter. But mostly I like that my drinking water isn't sitting in plastic.
Thinking of filtering your water? Check out these resources:
Which Water Filter System Is Right For Your Home? (Healthy Child Healthy World)
EWG's Guide to Safe Drinking Water (PDF)
EWG's National Drinking Water Database (including water filter buying guide)
Water filters: green buying guide 2/12 (Consumer Reports Greener Choices)
Green Guide's Water Filter Buying Guide (National Geographic)
5 Reasons Not to Drink Bottled Water (Mother Nature Network)