What would the difference be in using a 30W and a 60W version of the same solid state amp for miking up a guitar in a home recording scenario?

Which would produce a tone better suited for recording? Does it matter, or would you be able to get the exact same sound out of both of them by twiddling with the settings on each model?
If both amps have the same general tone, I would think you would not see a difference in sound when recorded. Generally, one does not crank a Solid State amp to max when recording. You don't get better sound the harder you push a Solid State amp.

If you need an amp with the flexibility to practice with a drummer or gig a small venue, you may want to go with the 60.
I'd go for getting a proper valve amp if you want tone, but between 30watt and 60watt in solid state amps, there will be little difference, but they'll be a bit quiet if you want to play live... for recording, they'll be alright though
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if its the same amp, they will ...or should...sound the same, the different wattage should only change the volume they can get up to.

Micing is the same for most amps, find the sweet spot on the speaker and use a good mic such as a Shure SM57.