Methanol or "Alcohol" as some refer to it, works well if you have high compression OR other need to eliminate octane related issues (spark knock). The Methanol (E100) has less BTU's then standard fuels so not as much power creation. You have to run a higher qty (about 30% ish more) to get the correct A/F ratio (around 8:1 vs 14.7:1 for standard fuel) so it's also not as efficient (thus why your E85 cars use more fuel too).
One benefit is that the engine runs much cooler to the point where you can actually run without a cooling system (we did that with the mini sprints and tractor pullers we put Vmax engines into AS WELL AS my older racecar).
NITRO on the other hand, short for NitroMethane, has the oxygen it mostly needs contained within the fuel and why top fuel cars basically run 95% or more fuel ratios and one missed ignition causes hydrolocking and nearly instantaneously pushing out of the spark plugs from the heads and or engine failure (usually catastrophic). Essentially a bomb contained within the cylinder.
People who make comments like "I have a bit Nitro shot" or the link you posted makes them sound very dumb to anyone with any basic knowledge of power adders.
Added some pics for your interest.