It is very different. Compelling one to fill out a ballot (even if it is blank) decays the right to vote into the obligation to vote. Paying taxes is an obligation. Choosing whether or not to vote is a right.
Agreed - 21 is absurd. I'd be curious to see the effects of lowering the drinking age (in the US) to 18 for those who graduate from high school (or equivalent). I honestly doubt we'd see a more-than-negligible increase in underage drinking.