Here's a thread that talks sense and then some.
Save for the voices above and below who sound more like Sales pitchers for whatever Smartphone Gimmick is out now than people with actual ideas or ability to understand how niche marketing works, you can tell who they are.
Will Smartphones destroy handholds? Fat chance of that, Nintendo's tops now and then, the big guy in the room isn't going to leave due to a bunch of smaller pissants running around his ankles trying to steal his cake. He'll just ignore them until they piss him off, then he'll crush them.
But, will Smartphones and gimmick games take a hit of handholds? Yes, a very BIG yes. You cannot deny the girth of the gimmick or casual gamer market, Smartphones will take a serious chunk of the profits, but until they actually make one with a usable Keyboard, mouse, and ability to run high end games they will never be anything more than gimmicks, which they are.
A Smartphone's major ideal concept, and the one I actually see a lot of people saying about it is thus. They have easy access to the internet, are good as phones, play games as a secondary function, and are considered socially relevant items. All of these factors combined, especially more so with Tablets(I own one myself) make them ideal and potentially threatening to handhelds.
The problem however is this, you cannot get a game with as much depth and complexity as say Chrono Trigger on the Smartphone or enjoy it. That's why FFVI on iOS is retarded, play the most iconic RPG of all time without a controller you say? Do Sabin's stupidly finicky Blitz moves with a touch screen you say? I say you're an idiot and your money is better wasted by flushing it down a toilet.
You can't get quality games without a controller, and touch screens will never EVER be good for anything more than gimmicks. You can't enjoy good RPGS on them, Platformers, pffh, good luck there, you can't enjoy FPS games on them, you can't enjoy Dungeon Crawlers, you can't enjoy anything substantial on them and Infinity Blade isn't that good either.
The sad fact of the matter is, that yes, the Youth play Smartphone games and will continuously alienate my generation thanks to the sheer amount of crap they've involved with and the growing disconnect felt by manchildren and neckbeards with society in general. But the even sadder fact, is no one will care in about two to three years when the next big thing comes in and replaces Smartphones.
Saying That smartphones will destroy Handhelds is like saying PC gaming will Destroy Consoles. Yeah, it's possible and I'm not gonna rule that out, but at this rate and in this highly competitive gaming market? Fat chance.
TL

R version. No phones will be replacing Handhelds for the time being, but if they can actually make something worthwhile that isn't a gimmick and prove that you can enjoy quality games and excellent narratives with a touchscreen thus elevating the genre; then I'll certainly say I can believe there's a good chance.