Whilst there are many studies comparing different approaches, the best one is one that is performed frequently by a surgeon. Often the anecdotal evidence can give you real life examples of the differences. Speak to as many people as you can about their experiences with total hip replacement surgery, and you will get a feel of what you would like.
It is preferably that you seek good results from a surgeon, whether it be via the direct anterior approach, or the posterior approach for the best possible outcome.
There are more than just the 2 approaches being used today - such as the lateral approach. Research shows that it is mostly comparable, but with issues with ongoing limp, however it is still being performed by some surgeons.
The research into approaches is still evolving, however most surgeons feel strongly about the approach they perform.