Here is an article that discusses the differences:
It appears Levemir is easier to tolerate a bit, but they are very close. Perhaps less reactions at the injection site.
I have seen some comments that Levemir offers some advantage.
But in the low dose range you use it may not be a big difference.
There is a suspected less weight gain with it (all insulins may cause weight gain--but at the low dose this is not so critical)
Levemir may cause less hypoglycemia at night...but in your low dose this may not be a factor.
People using high doses may require two Levemir injections per day. But you do not use high doses.
Less reactions at injection site for Levemir because it does not remain there in the tissue long like Lantus does.
So for you once a night dose would be the same, I think.