Approach depends on your surgeon's expertise and your particular case and your body. Each approach has its benefits and drawbacks and one isn't "better" than the other. Part of choosing the surgeon is trusting that they know what's best for our situation based on their training and experience. In my opinion it's something to be discussed if you have questions, but I can't imagine myself insisting on one or the other after reading a few articles in the interwebs and/or talking to someone who knows someone who...
Consider that with hip replacement, we can count the incision healing in terms of days, the muscles in terms of weeks, but the hip replacement in its entirety takes about a year no matter the approach. It's the final outcome that matters, not where you are in the healing process after several weeks or months.
Best wishes for finding a great surgeon.