Limber isn't the best because there's not many opponents that really inflict paralysis in USUM, and you can just use a Full Heal (or wait for Pokemon Refresh Affection to cure it for you). It is helpful in niche instances though, such as if you just hate paralysis with every fibre of your being and want it to never exist on your Hawlucha.
Unburden is equally mediocre because Hawlucha will likely be outspeeding most things in-game anyways, so the boost is pretty irrelevant. The only items you can really use in conjunction with it are Berries, because other consumables like the Focus Sash just don't make sense in-game. It can give Acrobatics a power boost, which is the one advantage I see it having, but Hawlucha is pretty frail and it 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 over the other. You can use either to equal success, as both are unlikely to make much of an impact on Hawlucha's battling.
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.
