Significant advantage? I would say not significant, but for me the advantages of the 9mm make it preferable for a carry gun.
9mm has the advantages of total capacity, reduced recoil, a wider selection of small concealable guns chambered for it, and cheaper *practice* ammo.
.40 has the advantage of a larger bullet with more muzzle energy. Also, even though .40 practice ammo is more expensive, you can usually find good SD ammo cheap on the Internet, cheaper than equivalent 9mm. Probably because of production overruns for LE sales that the manufacturers dump cheap.
With the right SD ammo, the performance between a top quality 9mm and top quality 40 is very close in standardized gelatin tests. A good apples-to-apples comparison is on Winchester's web site where you can compare their different Ranger series bullets:
http://www.winchester.com/SiteCollec...law_bullit.swf. Their test results don't show much differnce between the 9s and the 40s.
Of course we are rarely attacked by blocks of ballistic gelatin wearing 4 pair of Levis, but it's still an effective tool for comparing one bullet to another.
I own both a full-sized 40 and a sub-compact 9mm. The 9mm is my choice for carry while the 40 is the home defense gun. Go with whichever you prefer and can shoot well, you won't go wrong with either round.