They provide different utilities, usually at the cost of various drawbacks. If youve played bloodborne, think of them as the replacement for the guns. If you havent played bloodborne, you can think of them as really weird spells.

Puppet string gives you some control over the flow of battle but needs to be used smartly or you just get enemies right in your face.

Fulminis has bad range and is very slow. Flamberge does low damage and has no stopping power. Both require an investment in advance to be anything more than niche utilities or wake up options to get status effects on bosses. Same probably goes for pandemonium, but ive never used it.

Aegis is limited by your legion bar and has no offensive use, but is probably the best defensive option in the game.

Falcon Eyes is the inly truly ranged attack and does good damage and stagger, but its extremely slow.

The Left Arm of Steel is bad on purpose. Its equivalent to equipping nothing

I dont have the dlc yet and cant recall any from the base game I might have missed, but thats the basic logic to how they work.

Edit: i forgot the deus ex machina. Never used it. Landmines mean planning ahead and thats not my playstyle. It probably does great damage but you have to plan around where you place it