What does Hilton do better than Marriott? My experience, a few things:
1) IT - online check-in works. Digital key works. App has floor plans for most every property, which is awesome for those of us who are picky about our rooms. Online check-out works. Folios are emailed lightning fast and points now post within 24 hours.
2) Ease of getting decent status - Gold and Diamond are easy to get up front with a CC to cushion a soft landing from another chain if you can't match. You can have CC status for a year while you earn status the old fashioned way, then drop the card if you wish.
3) Extended-stay and lower-end brands - Hampton, Homewood, and Embassy are IMO better than their analogous MR brands. Full points earning on extended stay is real nice as well.
The one I really care about...
4) ROI. Look, I do 100 nights with MR and 75 with Hilton per year, and I like numbers. I've run my own personal numbers on ROI ($ value of redeemed hotels / $ spent on paid nights) and Hilton is on average 1.5X that of MR. Period. Marriott points earning levels these days are just sad, and while their redemption levels are lower at the bottom of the market, they converge with Hilton at the top. I just get a lot more value at the end of the day.
And one more, for fun...
5) Being second fiddle. Huh? But hear me out. My experience is that there are a lot fewer hardcore road warriors who are Hilton loyalists. Most of the big spenders are former SPG fans who haven't let go of the past. So MR properties are loaded with tippy-top elites and DYKWIAs. At Hilton properties I don't run into that as much - and in fact my upgrade percentage at Hilton is much higher (at former SPG properties half the time I feel like I can't even get higher than the 3rd floor, let alone an upgrade...). I can't quantify this, certainly not chainwide, but my experience is just that Marriott has mailed it in, knowing they have the post-SPG crowd locked in, whereas in the past couple years I feel like something has lit a fire under Hilton and they're actually trying.