Er ist nicht in der Lage ...
He is not in a position to ...
So that's more about the circumstances.
Er kann nicht ...
is about the (current or fundamental) ability.
If you want to say, that the little girl can't ride a bicycle (but she can learn it), you would use
Sie kann (noch) nicht Fahrrad fahren.
If you want to say, that young children are incapable of abstract thinking, you would rather use nicht in der Lage.
Kleine Kinder sind zu abstraktem Denken nicht in der Lage.
As an everyday expression kann nicht is (in my experience) more frequently used than ist nicht in der Lage.
In a more formal context you might want to distinct between skills and circumstances. It makes a difference, if you cannot do something because you don't know how
Ich kann nicht
or if you cannot do something because you are not allowed to do so or you don't have the access priveleges.
Ich bin nicht in der Lage
So if you want, you can use the one or the other to tranport a connotation. If a trainer is asked about the skills of a trainee, he might say
Er kann nicht streichen. (He cannot paint [a wall].)
meaning, the trainee doesn't know yet how to do it and will have to learn it.
If the trainer says
Er ist nicht in der Lage, eine Wand zu streichen.
it would rather mean, that he was tought how to do it, but all the time in the world won't make him a good painter.