The wheel is quicker than a series of locks (not important for leisure use) more expensive to build but it's probably cheaper to maintain than 20 locks.
I think the most efficient system to build and use would be a "bucket" and pulley’s attacked to a counter weight. Granted it would have far less summitry and not look as cool. The main advantage to locks is they scale really well but they use more water.
PS: I can't help but wonder how they counterbalance the buoyancy when one end dips into the water. Those curved tips might help and I can world out the geometry in my head but I think they just brute force it.
And it's in the Geek Atlas. It's wonderful. Art, engineering and education.
Search for Falkirk and you'll find it's been mentioned here before.
The only "demonstration of Archimedes principle" involved is that boats that float in water float in water.
It is seriously cool though.
