I would say smartphones have swept the leg on portables, but haven't delivered a killing blow. Some experiences are better on handheld whereas the main thing for smartphones is the games are cheaper, but 50/50 you're getting what you pay for. There's some fun super casual games that can be engaging as some portable games, but a majority lack the deepness (story, immersion, etc.) that you can get with portables. That's mainly down to the particular developer, but most really just get a game out that is similar to several others (the ones I actually enjoy--Kairosoft and the Sid Meier's Pirates-clones are pretty much identical to each other in their respective genres).
If I had to split up tablets and smartphones against portables, I'd say tablets would end up being the stronger competitor to that market and that's mainly because like portables once you have it, that's it. You have your Wi-Fi, you can play as you please and they're getting pretty competitive in price as well to resemble something of a competitor. With smartphones, you have that pesky bill thing and they tend to be rather expensive to get (unless you're getting a budget Android phone and you flash that bad boy proper).
In the short term business smartphones/tablets are giving portable trouble they don't have that rabid, diehard base like portables but they offer just enough to get the casuals who will be around for awhile. When it comes stand the test of time, 10 or 20 years from now barely anyone is going to tell their kids/nieces/nephews "Back in my day we had this game called Candy Crush and it was the CAT'S MEOW, I'll tell you what" in the same way you could say "Back in my day we had a version of Pokemon like that and Pokemon ruled the world for years."
EDIT: Oh yeah and buttons. Physical buttons over virtual buttons. My 3DS and my brother's Vita work perfectly for my...baseball mitt hands

but I'd have to either get a Galaxy phone or use the very tips of my fingers to use virtual buttons on some games.
...then proceeding to find your old handheld so that the young one can enjoy whatever title you mentioned. The one that is likely to carry on is Angry Birds, but like Candy Crush there's only so many times you paint the same game. It will work on casuals who may or may not buy the full version and invest in in-game currency, but not on your diehards who will invest in a handheld game's DLC/play a particular game for a long time (especially if there's an online multiplayer scene).