Depending on availability, I have had excellent results with both cherry shrimp (Neocaridina heteropoda (var. Red) and the Ghost Shrimp (Palaemonetes paludosus) AKA American Glass Shrimp, American Freshwater Shrimp with Axolotls and Cynops sp. as food for various caudates.
A few observations from my experience with them:
Amano Shrimp tend to be too big and too expensive.
In the case of Axolotls, I have witnessed Cherry Shrimp feeding on the gills. This made me a bit nervous, so the uneaten shrimp were quickly removed from the tank. Also Cherry shrimp are a bit pricey in my opinion for placement in a tank where they are more likely to become food.
With Ghost shrimp, axolotls loved them, and ate them quickly. Cynops sp. SLAUGHTERED the ghosties nearly as fast as I could drop them in the tank. I find the price and availability much more condusive to caudate tanks. The various sizes of these shrimp also make them suitable for the wide variation of mouth sizes in my collection. The Cynops all prefer the smaller shrimp.
As for using shrimp as "tank cleaners"... Nothing beats good tank maintenance practices. Yes, shrimp will eat detritus. Yes they will snack on various algae and other undesirebles like leftover food. Where the issue is, is that the shrimp will still output waste. Well, that and the more often become food long before they show any "cleaning" benefit.
Shrimp make a great snack for Cynops sp., but NOTHING beats regular water changes, properly maintained filtration and regular substrate siphonings.