I have NO practical experience, but considered this option, because I have been doing a lot of research in preparation for keeping marine fish, where sumps are very common. There were two motivations: firstly the second tank can have powerful filtration, but water flow in the main tank can be gentle which apparently suits axolotls. Secondly my tropical fish keeping has taught me to try and create a balanced system; we had an algae problem in our tank and my first thought was to add algae eating fish, but they would have been eaten by the axolotls. I wondered if algae eaters in the second tank would help a bit? Obviously the other tank can include other types of biological filtration.
The problem I saw was that sumps in marine tanks skim off the top layer of water through a weir and rely on there being substantial water movement (powerheads etc) to ensure all the water gets mixed up and goes through the sump. I wanted to get the water out of the main tank in this case from the bottom to stop it stagnating. My solution was a 'sump' above the main tank, where water was pumped from the bottom of the main tank into the other one and overflowed over a weir back, after being well filtered. The reason for this is that you need to ensure that if there's a power failure it doesn't overflow and a syphon from the bottom of the main tank could potentially deliver all the water to the sump if the return pump failed.
All theoretical, but I was thinking of giving it a try, ended up just buying a big tank!
Robert