Limber isn't great because few opponents inflict paralysis in USUM, and you can use a Full Heal or Pokemon Refresh's Affection to cure it. It's helpful in niche instances though, like if you loathe paralysis with every fibre of your being.
Unburden is equally mediocre because Hawlucha will likely be outspeeding most things in-game anyways, so the boost is usually irrelevant. The only items you can really use in conjunction with it are Berries, because other consumables like the Focus Sash aren't practical in-game. Its one advantage is boosting Acrobatics' power, but Hawlucha is frail and might get OHKOed if you're trying to proc its Berry in a battle.
Overall, a Pokemon usually has an Ability that's better than the other, but in your case, I legitimately don't see one having a noticeable advantage. You can use either to equal success, as both are unlikely to make much of an impact on Hawlucha's effectiveness.
Tl;dr Limber if you hate paralysis or Unburden if you have a surplus of Berries and like using Acrobatics, but it really doesn't matter whatsoever.
