Onedrive API vs LiveSDK

I am developing for WP8.1 and probably will port on other platforms. I want to integrate a OneDrive functionality, however, I can't understand what is the difference between LiveSDK (from NuGet packages) and OneDrive API.

It seems that Microsoft does not communicate at all regarding that, I really don't understand why. As far as I understood, the LiveSDK is the old one and will be replaced by OneDrive API, but the LiveSDK seems so much simpler to use that I can't understand their logic... On top of that both have been updated recently (in April for the LiveSDK).

So my question is

As long as my app has not been published yet, should I move to OneDrive API, or keep on the LiveSDK?
Does anyone has already tried both?
What are the limitations and benefits of both?

Based on a future-proof sight, I will go for the OneDrive API, but my main concern is:

Is is possible to login as easily on OneDrive API than with the Live SDK? (Working temporary solution below)

For now, I have been able to login with the LiveSDK using a single button and three lines of code, no user input required at all, where the AuthenticateAndContinue method used by the OneDrive API opens a Webcontrol and requires to enter manually the login and password.

At the end I have used the LiveSDK Authentication and use the access token provided with the OneDrive API. It is not a clean approach from my point of view, but I couldn't manage to get the AuthenticateAndContinue method to work (I get a 404 error answer after the login).

If anybody has a better solution, I am opened to suggestions :)

[Solution extracted from question to get out of "unanswered" stack]

In summary, my current method is the following:

Authenticate using LiveSDK API
Use the session cookie and the OneDrive API from there

The simplified code is the following:

The method below allows to log in silently, only the first time requires a manual validation from the user allowing the program to use its Live account.

It does not require any password from the user

var authClient = new LiveAuthClient();
var authResult = await authClient.LoginAsync(new string[] {  
        "wl.signin", "onedrive.readwrite", "onedrive.appfolder"});

if (authResult.Session == null)
    throw new InvalidOperationException("You need to sign in and give consent to the app.");

var Connection = new ODConnection("https://api.onedrive.com/v1.0", 
    new MicrosoftAccountAuthenticationInfo() { TokenType = "Bearer", 
    AccessToken = odArgs.Session.AccessToken });

It is not as clean as I would like (using 2 different SDK), but it works :)