If you don't have the right kind of oil you could burn out the motor.
The carbs on these usually have different mixture needles for idle and high throttle. You're either too lean or too rich on the high end. Read the owner's manual for method of adjustment.
Many of the newer small 2-strokes are starting to come under emissions regs, and have anti-tamper devices on the carbs, or offer very limited adjustment. You might find this is not possible. Engines this small tend to have carbs that vary widely as well from one to another. You may be stuck with the problem. It may have been a carb calibration compromise made for emissions.
It could be caused by too much oil. Plug could be fouled. Could be too rich or lean on the high speed adjustment.
Using 50:1 in the engine that calls for 40:1 *might* work. There has to be some margin of error there. But it may be lean enough on oil to seize it. Often times, if you don't run enough oil in the mix, you don't just have small problems. You don't know there's a problem until it's too late. You'll either seize it or score a rod bearing so bad that it will never run well again, etc. But where that margin is you'll never know until you go too far.
Safer thing would be to have the 40:1 used in both.