Level Ball: In order for it to be better than an Ultra Ball your Pokemon needs to be DOUBLED the Level of the Wild Pokemon your versing! When at any point other than post game when you're finishing the Pokedex are you going to be double the level?
How about if you're Pokemon is higher Level it's a 2x plus 0.1x for each additional level higher (max at 8x). Also, maybe have the Pokemon gain double Experience if its not the highest Level Pokemon in your party. Make it into the "catch up" Ball for Pokemon you want to use but you would have to grind since their Level is very low compared to your current party.
Lure Ball: Oh, they did update some! Lure Ball is now 5x for fished up Pokemon. Very nice... too bad we can only get at mos two...
Moon Ball: Only useful on Pokemon who evolve by Moon Stone. All of SIX Pokemon. Well, if they're all in the Regional Dex. Let's just make this the "night" ball. No, I don't mean useful for catching Pokemon at night, but rather Pokemon affiliated with the night as well as the moon: Pokemon who evolve via Moon Stone, evolve via Dusk Stone, evolve at Night, can naturally learn Moonlight or Moonblast, only come out at night, or are moon-related (Umbreon, Lunatone, Cresselia, Darkrai, Lunala). Granted, still very niche, but better than what it was. Plus I imagine these are the only Pokemon you'd use it on anyway (caught my Lunala Nebby in a Moon Ball).
Friend Ball: Sets Friendship to 200... it already has a limited us, might as well have it max out Friendship and prevent it from lowering. Would it also be too much to suggest it teaches Return upon capture?
Love Ball: Problem here is the ONLY effect is 8x against Wild Pokemon the same gender AND SPECIES. How about adding a 3x if the wild Pokemon is just opposite gender and 5x if opposite gender and same Egg Group. Also maybe extend the same Species to include the evolutionary family (and possibly related Pokemon, like it'll be x8 on a wild Tauros/Volbeat/Nidoran (m) if you're using a Miltank/Illumise/Nidoran (f) and vice versa). Also, maybe have the Pokemon sent out afflict Attract on opposite gender Pokemon in wild battles. Why not? As long as it doesn't alter Trainer Battles.
Heavy Ball: I never understood why its modification was addition and not multiplication. Worst, it's only useful on a small handful of Pokemon, even with SM's update of it. They just need to redo it. Use multiplication, and come up with a chart that's also a bit more lenient. Like below 10 kg is 1x, 10-24.9 is 2x, 25-49.9 is 3x, 50-99.9 is 4x, 100-199.9 is 5x, 200-399.9 is 6x, 400-799.9 is 7x, and 800 above is 8x.
Fast Ball: Like Heavy Ball, it's requirement is too high: base Speed needs to be 100 or above for 4x. That's not a lot of Pokemon, or at least Pokemon available in the wild. How about below 15 is 1x, 16-30 is 2x, 31-45 is 3x, 46-60 is 4x, 61-75 is 5x, 76-90 is 6x, 91-105 is 7x, and 120 above is 8x.
Premier Ball: Normally I think Premier is fine as is, a little bonus for buying 10 or more Poke Balls (though that should go for any type of Ball), but I thought it would be neat if maybe they gave it a "secret" catch rate modification: 8x on Shiny Pokemon. The Premier Ball is sort of like a Shiny Poke Ball, so why not?
Repeat Ball: 3.5x at catching Pokemon you already caught, ~whoo. First, make it 3.5x for a seen Pokemon and 7x for a Pokemon you caught. Also, maybe have it so that if the Pokemon in this Ball is the first in your party it's more likely the encounter will be the same species. Let's not waste time here, only reason you'd do this if the Pokemon you caught didn't have the Ability or Nature you didn't like or you'll looking for a Shiny.
Timer Ball: Fine as is but I don't think it should be capped.
Nest Ball: Works better lower level Pokemon, aka copy of Level Ball. Scrap that, just make it just 3.5x against Pokemon in the Flying and Field Egg Group.
Net Ball: Fine, though to not overshadow the Dive Ball I would suggest it caught Pokemon in the Water 1 and Bug Egg Groups instead.
Dive Ball: And it'll be 3.5x on Water 2 and Water 3 Egg Groups.
Luxury Ball: Copy of Friend Ball. To make it different, instead I would make it double a Pokemon's Affection, Fullness, and Enjoyment value in Pokemon Refresh.
Heal Ball: Fully heals, cures, and restores all PP of the Pokemon caught in it. How... useful... How about this, at the end of battle it'll cure the Pokemon of any status ailment (save a trip to Pokemon Refresh) and doubles the effect of healing and PP restoring items used on it. It's the resource conscious Pokemon.
Quick Ball: Fine as is, though if I were to make a change I'd have it decrease by 1 for every turn after the first until reaching 1x.
Every other Ball is fine.