The amiibo figures will be successful because instead of making the game playable, they add to the already awesome game. Plus, they can be used in multiple games like Mario Kart 8, Super Smash Bros., and Hyrule Warriors. While Skylanders are necessary to have if you want to both play and 100% complete any of the Skylanders games.
Nintendo has a long history of fan support. The number of IPs Nintendo owns gives the company a significant advantage over Skylanders. Also, incorporating Amiibo into various Nintendo software such as Super Smash Bros. will provide more unique opportunities for the figurines. Finally, the Wii U is built with an NFC chip which makes incorporation of Amiibo much easier than Skylanders or Disney Infinity, which both require a separate attachment for implementation.
Skylanders are a runaway success, and many companies have jumped on the bandwagon in order to cash in on the craze. There are already many popular brands that give Skylanders a run for their money, such as Disney Infinity, and any other franchise with recognisable characters is bound to be a success with fans of the genre who enjoy the collecting aspect.
Yes, the new Nintendo figurines will give Skylanders a run for their money, because Nintendo has such a long life and fan base. We will never forget classic Mario, and all of the characters, like Donkey Kong. They have done a good job of continuing to reinvent the characters as the platforms have changed.
Like the infamous broken game called Disney Infinity, Amiibo would not have existed without Skylanders. Even at that, Amiibo sucks at trying to one up on Skylanders because Skylanders bring the game to life, Amiibo does not. Not only that, not even half of the Amiibo have a corresponding game. Ammibo fans are a huge part of it too, because some people like to sell a little plastic toy that does NOTHING without its game, for over 800 FREAKING DOLLARS!
I don't know about you, but I hate cheap knockoffs.
Nintendo has some iconic characters, but most people aren't going to buy into another Skylander's type game. Nintendo doesn't have the clout that he used to have, unless they can change their image it isn't going to go as far as Skylander's have. It just isn't in the cards for them.