We switched the same way about a year ago and saw no difference. As a note, though, we were still in honeymoon.
Basaglar to us works exactly like Lantus, so it would be an easy one-to-one change. Levemir works the same way for some, but does not work as long for others. As for Tresiba, as I am sure you know it gives you hyper-stable basal, with fewer lows at night in particular, but may be more of an issue when you need to change basal often, since it remains active for about 2-3 days.
Imho, the easiest swap is to go to Basaglar, but Tresiba could be a great option.