Certainly, it has been my experience that characters level much faster in 3e that they did in 2nd Edition. 2nd Edition was about the same as BECM D&D.
(My understanding is that 4e PCs are generally expected to level up almost every session, but that with 30 levels to gain the length of the campaign should be about the same. However, that's based on hearsay, not actual play experience.)
That said, it depends very much on the campaign, the group, and even the levels themselves.
As I've gotten older, it has become harder and harder to get the group together. That means that we have to make the most of what gaming we do get in, and it means that campaigns have had to be accelerated to compensate. As such, it is no longer feasible to root around for 4-6 sessions at 1st level - we want to get up and on to the "good stuff" as quickly as possible.
And, in fact, it has always been my preference to get through the first few levels as quickly as possible. I don't like just omitting them, as I find them very useful for establishing character, but at the same time I don't want to dwell overly on them. However, once 2nd Edition characters got to 5th level, or 3e characters got to about 4th, I preferred to slow advancement somewhat, to draw out the "sweet spot".
(I've also started moving very strongly away from giving XP for defeating challenges/killing monsters/gathering treasure. In my recent SWSE campaign, characters simply levelled up every 1-and-a-half sessions, either at the end of the session or at our 'break' for food. I would do the same for D&D, except that the spending of XP for item creation makes this difficult.)