Super Saiyan God 2 is the 'true' successor to Super Saiyan God as it is purely God Ki based rather than Super Saiyan Blue as it is a combination of Super Saiyan and Super Saiyan God.
How it's obtained...
Super Saiyan God 2 is obtained by training the powers of Super Saiyan God in a traditional sense under extreme conditions rather than combining the powers of Super Saiyan God with Super Saiyan. Just as how Super Saiyan 2 follows Super Saiyan, Super Saiyan God 2 follows after Super Saiyan God. This form is first obtained through anger as most Super Saiyan forms are.
Appearance
Super Saiyan God 2 bears a striking resemblance to its predecessor, Super Saiyan God as the only difference is its spikier ends and its orange lightning within the aura of the user. The form retains its fiery appearance along with the eyes remaining red and gaining noticeable pupils.
Usage and Power
The form is solely powered by God Ki just as it's predecessor. This form multiplies it's already boosted healing and recovery rate that it gained from Super Saiyan God, by 2. This form also multiplies the ability to absorb and nullify enemy attacks upon contact by the same factor. Super Saiyan God 2 also cuts the stamina drain in half while simultaneously multiplying the capabilities of the previous form, such as speed, endurance, and power by 2.
Super Saiyan God Vs Super Saiyan God Super Saiyan(Blue)
You might be wondering how the might of Super Saiyan God compare to Super Saiyan Blue and the simple answer is... not at all. Super Saiyan God 2 is twice as powerful as Super Saiyan God but Super Saiyan Blue is 50x the power of Super Saiyan God not counting the major boost in power that extreme Ki control the form is known for. Considering all the evidence, Super Saiyan Blue vastly outclasses Super Saiyan God 2.