Easiest way to see whether these two graphs are isomorphic 
I've tested a few isomorphic invariants such as total degrees, total vertices, total edges, total amount of degree $4$ vertices and so on.
It seems that it holds for a lot of the isomorphic invariants.
Is there a good efficient way to check in general if two graphs are isomorphic?

There's no efficient way known in general. For these small graphs, you could look at the two vertices of degree $2$. In one graph, they share one neighbor, but in the other they share two.
