So thanks to the recent eShop release of Metroid Prime I've had a chance to experience FPS controls on a Wii remote, and I have to say it's probably the best you'll see on a console. With sensitivity turned up to "Advanced" you have a rough approximation of mouse aiming that more than does the job, even without the generous auto-aim that this particular game came with. I honestly think this was a much better step forward for gaming than the successor, the Wii U's unwieldy tablet controller thing.
I should note first off that the Wii U's GamePad isn't necessarily a bad controller, except for maybe the dismal battery life. I am, however, saying that it doesn't really justify itself. Nintendo made a whole bunch of promises about a future involving asymmetric multiplayer and the new gameplay opportunities brought to the table by having a second screen in the mix. I don't personally feel any of these opportunities actually showed up in a compelling fashion. Hell, when Nintendo did try to base games around the GamePad, we managed to make WarioWare into a turd!
(Okay, my mistake: Game and Wario was probably the second bad WarioWare game. The first being Snapped, which was a DSiWare exclusive and thus difficult to remember.)
The Wii remote is a very versatile controller by virtue of it's shape and button placement. On it's side it is roughly an NES controller with a few extra buttons; held like a remote it is roughly a presentation mouse with a D-Pad. With the addition of motion controls and an IR camera for pointing, we have enough inputs to allow a wide variety of games to be controlled using the system. If you need even more controls, then go grab a Nunchuk attachment for an analog stick, two more triggers, and extra motion inputs.
In contrast, the best we can say about the Wii U GamePad is that the addition of a touchscreen didn't take away anything from the bog-standard dual-analog controller setup that it's tied to. But if we made the touchscreen stand alone for itself, it would be a ridiculously horrible experience. Many games flat out won't work with a touchscreen, or become surprisingly difficult. The entire history of the iOS App Store with regards to games for the first few years of it's existence is littered with failed attempts at porting traditional games over to a touchscreen. The best you can do is get a large touchscreen, litter half the screen with virtual controls, and stop caring about tactile feedback or input latency.
The GamePad represents, at it's core, a schism between a desire to appeal to both the hard-core and the casual at the same time while still adding something "unique" to the table. It has a standard compliment of inputs that scream "tablet" and "motion", intended to be familiar to an audience that Nintendo lost to Apple when development of Wii U started. And it also has a standard compliement of inputs for the "hardcore gamer"; dual analogs, D-Pad, face buttons, and triggers for the audience that Nintendo lost to Sony when development of the PlayStation turned into a stand-alone console. And from what I've played of the system 80 to 90 percent of games on the system are perfectly content to just pretend the tablet part of the GamePad doesn't exist.
A particularly telling example was about an hour ago when I was playing niche puzzle game Color Zen, which uses the touchscreen exclusively. I realized that everything done on the touchscreen could just as easily have been done with a Wii remote, except with the added advantage of not having half the screen obscured by my big meaty American hands. (This is actually more of a problem than one might think)
If Nintendo really wanted to ensure a full compliment buttons to improve porting from other consoles, they could have at least done one good thing: use the GameCube controller's buttons. The GameCube controller was a prime exercise in designing affordances into your hardware and it's a shame future Nintendo controllers of this vein are practically indistinguishable from dual-analog controllers from their competitors. Every button on the thing is a different color and shape; and they all have different tactile feel. You can easily tell new players what buttons do what just by these physical attributes instead of a set of four physically identical face buttons.
(Also, the GameCube controller had analog triggers, a feature which was strangely removed from future controllers starting with the Classic Controller Pro.)