Marginally the same appeal as .45 but with more mag capacity. Does come at the downside of being a little snappier, but anyone who whines about that is pretty sad; if you can't control a .40, you have no business shooting at all, IMO. Personally, I think it comes down to what you shoot best. I like .40 just fine. I don't bother with .45. If 9mm is better than .40 because ammo advances have made it good enough to do the job, but with more ammo in the mag, it's certainly reason to go with it instead of the .45 as well.
In my estimation, there are a few things worth looking at when it comes to choosing ammo. Number 1 consideration is how well you shoot it. Anyone reasonably competent should be able to put rounds on target with any of the 3, so it strikes me as mostly a wash, with difference being minor. Number 2 consideration is lethality. This is where you get lots of disinformation. If you look up the studies that have been done collating evidence of actual gun fights with the weapon reported used, across all 3 major calibers, it took a little more than 2 rounds to stop the threat. The interesting thing, however, is that the same was true for .22. In fact, a couple .22 hollow point rounds can create a virtually identical wound channel to a popular 9mm hollow point. Penetration? Also largely equivalent across the board. Knockdown power is a total myth. Putting a bigger hole in a guy? A myth. The difference between a 9mm and a .45 is insignificant (less than a tenth of an inch). Shot placement is everything. Size of hole is negligible. The .22 LR and the .223 Remington/5.56mm NATO are the same caliber. Both are .22's. Both put the same size hole into the target. One hits with a heck of a lot more energy, however. Energy across 9mm to .40 to .45 is pretty comparable as well. Ultimately, if you think that .40's are worthless because of 9mm, you should think that .45 is worthless also, for exactly the same reasons. And, realistically speaking, you could make the same arguments about .22LR being better than 9mm. The one thing that turns me off of .22LR as a carry caliber (although I do have a backup piece in .22LR), is the higher failure rate of rimfire ammo as compared to centerfire.
For these reasons, all other things being equal, with ammo advances having made the 9mm a perfectly competent round, I'd rather carry a 9mm than anything else, especially because rounds are normally cheaper. However, I do keep (and carry) .40's on a regular basis. Why? Because in a Democratic presidency, ammo shortages may be concerns. 9mm and .45 both were impossible to find on shelves, but I could always find ammo for my .40's. Your 9mm is useless if you can't feed it. I want to always be able to practice with and have carry ammo for my guns, so I keep one in each caliber for a carry piece.
My 2 cents...