What are the differences between a x1 and a x10 osciloscope probe

The pro is that a 10x probe has 10x the input impedance so will interfere with the signal being measured less. The con is that it is reducing the voltage on your signal by 10x before it reaches the scope so it cannot measure signals with very low amplitudes or measure with noise levels as low as a x1 probe will (your scope introduces noise and if your signal is 10x smaller when it reaches the scope, then the noise of the scope will be 10x bigger than it would otherwise relative to the signal).

But a side benefit of stepping down the voltage by 10x before it reaches your scope is that you can measure signals with a maximum amplitude 10x higher.

Use x1 probe to measure very low amplitude signals in low impedance circuits. Use 10x to measure everything else, especially if the circuit being measured is higher impedance. If your circuit is low amplitude but high impedance...well...that's where it gets tricky.

Use probes more than x10 if you need to measure voltages that are higher than what your scope can accept with either a x1 or x10 probe.

I don't like to use a x1 probe with anything I know will be more than 50V, even though a scope input can typically directly accept 300V for oscilloscope preservation purposes. I use a x100 probe for anything larger than 100V for the same reason. You never know what overshoot might exist in a signal you are measuring.

A downside is that it divides the voltage by 10 and thus the signal is weaker at scope input. So there is a limit how small signals can be measured, but it depends on the scope. If the amplitude is too low for 10x probe, and if it is known that the dowsides of 1x probes do not prevent measurement, then a 1x probe can be used.