This eventually comes down to preference. In my opinion, one does not work "better" than the other. They both do largely the same things. Picture one carpenter building a house using centimeters and meters measurements and another one uses inches and feet. They can build the same house, but they just use two different units of measure to get there.
All that said, I tend to gravitate toward mils for timed competition events because I like the smaller firing solution numbers that I have to remember when running mils vs. MOA. It is more intuitive to me and easier for me to remember when I'm more stressed out from being on the clock. For example, I just shot a 3-gun match last month and I knew that my 5.56 carbine shot pretty much dead-on out to 200 yards, so I did not correct for elevation out to that distance. From there, my 300 yard hold was about 1 mil, exactly. My 400 yard hold was about 2 mils, exactly. This made those long shots much easier to holdover for in a hurry than they might have otherwise been if I were trying to remember holds like 3 1/4 MOA and 6 1/2 MOA instead. I also know from experience, this intuition crosses over to dialing come-ups also, not just holdovers.
Again, this is a personal preference of mine and it certainly isn't the only way to do it. There are plenty of phenomenal competition shooters out there running MOA. I encourage you to seek out opinions from others as well and I hope more people chime in on this topic and offer their thoughts, too.