For each of my builds:
Vladof - 1340 shield (The voice commentary is worth the lower absorb rate than the Sham for me)
Bandit - Hide of Terra (Great for steamrollin’)
Hyperion - Amp shield (I use a nerfed version of the Bee and prefer the Amp shield’s mechanic)
Maliwan - Black Hole (Maliwan makes so many good ones… I’d probably have a different answer tomorrow)
Torgue - Big Boom Blaster (feed me rockets!)
Dahl - WTF (Shield is meh, but I love the boosters)
Jakobs - Blockade (Jakobs only Zer0 is too fragile for my taste with the Rough Rider)
Tediore - Quick Shield (Built like the Cracked Sash, but with elemental resistance)
Rough Rider cause shield capacity is for babies. Plus it negates some of the self inflicted damage caused by “Silence the Voices” on Krieg.
I’d have to go with the rough rider on Maya I mean there are some great shields I use all the time with her when Im actually fighting enemies (bee, sham, negotiation, etc) but that movement speed increase can’t be beaten
The 1340 Shield is nice! I thought I was the only one using it, even though I only use it in normal mode while leveling to help with the Ammo Eater challenge.
I’ve always used it as my maim absorb shield regardless of play thru until I get a The Transformer shield (or on 3 occasions, The Sham…).
My favorite shield is the cracked sash. Hands down best shield ever for gunzerker.
You’re kidding right ? 
It’s not even the best Tediore shield
Cradle of course, it does INSANE damage on OP8, Gearbox should surely nerf this along with Kunai and remove Raving Retribution Voice lines. I mean seriously, what shield can compete with the Cradle? Hide of Terra, pffft. Sham? HA! The Cradle is a true hero and a real shield.
(Can’t believe you guys fell for it, in all seriousness I’d say the Rough Rider because I play Krieg alot)
Whiskey Tango Foxtrot can compete. Who wouldn’t want spontaneous shock MIRVs all around them during a firefight?
I’ve come to love the WTF shield, but it took some practice to get the reflex down to catch the booster right as it spawns reliably (if I don’t want the IEDs). Not that it’s hard to catch them, but with other booster shields, it’s not really a big deal if you miss one - you can go get it later if needed, no harm, no foul. If a WTF booster gets loose when you don’t want it to, it can obviously mean death. When you let a booster go to drop those shock IEDs in a field of enemies, it can kill them (usually spectacularly). It is situational though - I wouldn’t use it against flying enemies, Crystalisks, or against lone rabid enemies, for example.
What makes the WTF shield work where The Cradle doesn’t is that while I think their aiming routine is about the same, the WTF IEDs have a huge damage radius (so they just need to get near an enemy to do damage), and they do lots of damage. The Cradle’s IED has to hit directly (rare), and when it does, the damage isn’t much. See also: the Asteroid Belt (a Cradle done right, in my opinion).
I think that the damage of both (Asteroid Belt and The Cradle) scale poorly late in the game. If the damage of the Cradle was noticeable I would totally use it with Axton with a splash setup.
Just imagine it with all of Axton shield buffs and grenade damage.