In terms of their physiology, tegus are pretty typical lizards, while monitors are a bit more like mammals. Like most lizards, tegus are unable to breathe while running, because of the way their chest flexes as their forelegs move. Turns out it doesn't much matter, because tegus, like most lizards, rely on glucose stored in their muscles and run anaerobically. Their leg and back muscles are pale ('white meat', like chicken breast), and like chickens flying, they tire out pretty quickly.
Monitors can breathe while running, and use aerobic metabolic pathways almost all of the time. Their muscles are red (from myoglobin, which stores oxygen), same as the leg muscles of chickens ('dark meat", eh). Like chickens running, monitors can go a very long way before they tire out.
The difference then is between "burst" speed and "endurance" speed, and monitors would win any race. This hasn't a whole lot of relevance to keeping either tegus or monitors in captivity, except to note that cooling a monitor down does it a lot more damage than does cooling a tegu. Tegus can shut down metabolically and pop back once warmed up again, while for many monitors this would pose a major physiological problem. Oddly, the main place that tegus have aerobic (red) muscles is in their jaws, and many people can attest to the point that a tegu can bite and hold on until Sunday if it chooses, whereas monitors are more likely to let go in a half hour or so.
This is also why tegus are better eating than are monitors, unless you like that gamey flavor that comes from myoglobin.