The only hint we got that Eccleston had recently regenerated was his comment about his ears when he looked in a mirror in "Rose." I'd sort of assume he'd maybe regenerated at the end of the Time War.
I know that at least before "The Next Doctor" was cast there was discussion about David Morrissey playing the 11th Doctor, and I think he would have been brilliant, and some how a more logical follow up than Matt Smith to Tennant's doctor. Morrissey has been good in everything I've seen him in (Blackpool is a don't miss, he and Tennant play "enemies" and are hilarious together). But I guess Moffat wanted to go in another direction with the Doctor.
Smith's Doctor is much more alien and quirky, but not nearly as deep emotionally I think, as Morrissey would have been.