Sorry, but a Wii U is not going to be able to do everything a Wii does.
A Wii U has no support for real GC Memory Cards, and several GameCube games have problems with emulated cards on Nintendont, so you're screwed there.
A Wii U requires an accessory to use GC controllers that takes
two USB slots, while the Wii has all you need integrated into the system. And not using original controllers can be annoying with games that made use of their pressure-sensitive L & R Triggers.
As far as I know, the GBA- GC cable does not work on Wii U either, but it does on Wii, so you'll be unable to use the features on some games, like Zelda Four Swords, the Sonic Adventure games, Pokémon or Final Fantasy Crystal Chronicles.
Wii U as far as I know cannot output 240P, which a whole bunch of people playing retro games care about quite a bit, specially people with CRTs.
I also read on the shmups forum that Wii games on Wii U
actually look worse than playing on original hardware.
There are more things, but those are the ones I can say from the top of my head. Bottom line is that vWii mode capabilities on Wii U are not entirely the same as a genuine Wii. Yesterday I saw Wiis being sold for 20 euros here, with cables and everything, so they seem to be very affordable if you want one. Softmodding a Wii is very simple and the benefits are gigantic, there's simply no reason for not doing it, even more in this day and age, and the Wii is still great for an emulation machine, specially because besides emulation you get native support for two entire system libraries for such a low price. If you end up wanting to get one, here's a tip: Buy a Wii that's red, black or blue to be sure you get a good revision.
Also, I find Wii homebrew to be quite a bit more stable and less dangerous all around, but I don't have nearly as much experience with Wii U than I have with Wii.
Now, the Wii U has its own good unique points, and it can make for a great emulation machine too, don't take this post the wrong way, but make no mistake thinking that a Wii U makes a normal Wii obsolete, because that's just not true. Specially if you care about GameCube stuff.
I would invite you to read around here and other places on the net to make the decision, although, as I said, with the Wii being so cheap and all around useful for what it is, getting one won't hurt you; and getting both wouldn't be much of a hassle either if you collect systems.