First thought is fuel delivery. It sounds like it's fuel starvation or leaning out the mixture. Air/vacuum leaks? Best to run on the rich side of lean. Could be a bad coil too, like desert rat says. ETA: If the fuel mixture is too lean, you could be running too hot and overheating.
Cool pics but the front wheels on the larger kart look troublesome. Were those bought as a tire and wheel assembly {i.e. together}?
Harbor Freight sells a tire and wheel combo like that but it is not meant for any powered vehicle--it's meant for carts, not karts.
Those are light duty only and will self destruct in short order. The bearings are junk too, not anything like precision sealed bearings.
A final word on the pedals on both karts; they are mounted backwards. Now they
can be mounted like you have them, for a fella of short stature to reach the pedals better but mounted so that they arch forward, they provide a built-in foot rest for the outer edge of the foot to lean against. Mounted correctly, they provide a more comfortable operating angle, for sure. This configuration also helps keep the feet away from the spinning [
danger, danger} wheels. Here's an illustration of a proper throttle pedal: