Do cleaning tablets work as well as liquid detergent?

For the same active chemistry, yes — what you are buying is less water and less plastic, and the risk is people using them at the wrong dilution.

A tablet is a concentrate with the water removed. Dissolved at the stated volume it behaves like the liquid version, and the environmental case for shipping less water is real.

The failure is dilution. Dropping a tablet into a smaller container than the instructions specify gives a stronger solution, and on natural stone or paintwork that is where the damage comes from.

Check the tablet is intended for your machine. Some floor washer and steam machine makers void the warranty for anything not in their own list, and tablets designed for a bucket may foam badly in a recovery tank.