I say get them both! They'll be all you need to finish the offline game.
In terms of damage output, on weapons with high element ratings, AUM+Elem Up matches AUL/Crit Eye. So for elemental LS and SnS, Lagi is hands down better, since Razor Sharp is great for them. If you're lucky in offline/LR, you might get an Attack +6 (or one slot/Attack+5) talisman, which can bump Lagi up to AUL, and then it's no contest.
If you're playing online, both Lagi and Los are also quite good in high rank when overforged. I got through the 4* quests with overforged Lagi, Los, and Bari sets pretty quickly - it only takes a few hunts to overforge a set. I didn't make any of the + versions until I got past my 5* Urgent, when better yielding quests for rare materials become available.