MVC is a design pattern with aim to reduce coupling and increase cohesion of the UI, there are many different flavors from it such as MVP and MVVM.
Currently the trend is not to build a dedicated interface for each device platform, but to use something called responsive design (ex: bootstrap); this was possible after the release of CSS3 media queries, allowing your interface to adapt to the device it is being used on, also you can use bootstrap which is a very good UI framework that provide you with out-of-the-box responsive behavior CSS.
So bottom line (options using MVC):
responsive design: you'll be returning the same view allows and the CSS3 HTML5 will be responsible to adapt to device type.
controller device detection and multi views serving: your controller will detect the browser type and device;accordingly you'll be served a view that address you need - example if you open from desktop index will serve you IndexDesktop, if mobile the same model will be created the same item but will return IndexMobile. (to detect the mobile device and stuff go and download c# code)
dedicated sites: which is not what i recommend because you'll be repeating your self in every move and would duplicate the amount of work.
Is MVC a wise choice in this case or which is the 1st stop for this kind of xdevice web app?
Personally I would recommend you go with a solid MV* framework; which one this is totally your call, you can go to MVC and it'll help you select one, I personally recommend using angularJS backbonejs or emberjs, they are all really nice and solid to work with, ASP.net MVC is a real nice framework but the problem is when it come to client side work, the framework will start to become problematic.
EDIT: Why ASP.Net MVC is a bit problematic when it come to client side?!
I personally use MVC4 for web development, and the number of things that you can do using it, is amazing; stuff like web API, testing, dependency injection, the out-of-the-box stuff like asp.net identity, but when it come to internal page routing, caching, handling internal page ajax, you'll need to use something other than razor.
most of the time i use MVC .net with some client side framework for optimum behavior, the result become something like a hybrid solution which the best from both sides.
Check this website out Hot towel - angular