Two totally different things, like Rob said.

Meth works to prevent knock which allows you to run more aggressive timing and higher boost levels. It basically burns like a higher octane fuel than pump gas and it cools the intake temps which also suppresses knock.

Adding meth to your car RICHENS your tune, it is a fuel.

Nitrous is an oxidizer it LEANS your tune, it is a power adder but you need to add more fuel to compensate for it. It also cools your intake temps similar to meth.

I'm certainly not an expert, but that's how I understand it.

Either way you'll need a tune, meth is more of a cheap replacement for race gas whereas nitrous is a power adder by itself.