A precautionary landing is nothing to do with a low-level circuit. One might do a precautionary landing if caught by bad weather and if the cloud base is low, one would do a low-level circuit (having inspected the field first). One also might wish to land asap if the engine is faulty, you are running out of fuel or your are feeling very ill.
Bad weather circuits come in two types. One might opt for a high level circuit if the slant range viz is duff (or a very low inversion). Then a 2000 foot circuit and steep approach may offer better views of the landing strip. I did one once at night when the viz was 50 metres ( I had nowhere else to go), but I had a perfect view of the runway until almost touch-down.
A low level circuit is performed when the cloud base is low or the viz poor. That is done normally (if possible) a 100 feet or so below the cloud base, with approach flap selected. The track over the ground is much tighter than normal. The base leg turn is flown level until one intercepts the normal glide path. That will require more power than normal. Moreover, because the angle of bank around the finals turn is perhaps more than usual, then drag will be higher as well as the stalling speed. More power is thus required.
All good fun, but if you practice either, do tell the tower and watch/listen for other aircraft flying a normal circuit.