My group has done slow advancement for every game so far.
It gives the DM quite a bit of leeway for ramping up challenge, especially for a well-optimized and/or large party.
Our group has completed Kingmaker and Serpent's Skull; we were usually 1 or 2 levels behind the recommended level, but made up for it by being a larger group (usually 5 to 7 players are any given game).
So far it's worked fine.
I've played in a group that did slow advancement and it was pretty awesome. We'd play an average of five sessions or so before we gained a level, so it had a more 1E-2E vibe to us (when it was typical to gain a level every three to five sessions or so). It was a blast for us.
But I don't think that everyone would enjoy it that way. It seems that most groups these days enjoy leveling at a bit faster rate than that. Heck, I don't know many groups these days that even do individual x.p. awards any more.
In actual play, our biggest net effect was that we went through disposable magic items (potions and scrolls) a bit faster--more encounters per level and all that. My observation is that around 20% or so of the treasure at any given level is disposable at fast advancement, around 25-30% at medium, and 30-40% at slow. I'd recommend that you discuss disposable items with your GM before the campaign starts, especially if your party is the sort that likes to rely on them. Treasure from individual encounters were also correspondingly smaller, but it wasn't really noticeable over the long haul.
I've never played slow. My feeling is that if you think you want to play slow, what you really want is to play E6.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.