My preferred method is to mic up the amp, though there’s no harm in trying other methods and seeing which gives the best results.
Note that if you mic up the amp, the microphone position will make quite a lot of difference. Having the microphone close to the speaker will generally give you more bottom end (using a cardioid/directional microphone) - placing the microphone off axis, toward the rim of the speaker may pick up more overtones. If your amp is an open back design you can experiment positioning the microphone at the back of the cab.
A common mistake is to overdrive guitar amps too much, resulting in a waspy sound with no real definition. The most powerful guitar sound is not the same as the most distorted.