Approval voting then is just a "restricted" subset of "relaxed ranked choice". That is, any preference expressed in an approval voting ballot can also be expressed in a relaxed ranked choice ballot. Similarly, relaxed ranked choice voting can be considered a restricted subset of range voting. And our traditional "single choice" voting can be considered a restricted subset of all of them.
And really you should separate the mechanism for expressing voter preference from the mechanism for picking a winner. Those are separate things that, in theory, can be mixed-and-matched to produce various voting systems.
So, clearly range voting is in some sense the best (or tied for the best) ballot, in the sense that it allows the voter to express a range of preferences that is a superset of the other systems.
But there is also the issue of ballot simplicity. Some people might prefer the simpler ballots of the approval system, or even the traditional single choice system. But since those ballots have corresponding "range voting" ballots, you can deploy a "range voting" election while allowing voters to use the kind of ballot they are comfortable with.
Indeed you can imagine the idea of a "progressive ballot" in which the voter starts of with a simple "single choice" ballot, and can optionally refine their preferences with an approval ballot, then a ranked choice ballot, then, ultimately a "range" ballot.
I've actually implemented such a thing [1].
[1] http://macd.tk/pollplace - Note, this is running on an underpowered test server not intended for public use, so be gentle.