I've always favored registration fees by weight, but I think they should be progressive, with each added pound costing you more than the previous one. That's sort of the way most household utility bills work, with a lower rate for lower consumption.
Diesels are cleaner inasmuch as they feature inherently more complete combustion than spark ignited engines. They're sootier for sure, and they stink, but their exhaust is poor in partially burned hydrocarbons compared to gas cars. Carbon monoxide doesn't smell, you know? Diesels got catalytic converters much later, because there wasn't nearly as much work for them to do.
When I get smacked in the bike lane by fumes that make me want to go home and lie down, it's always gas. Gasoline cars have the ability to run super dirty. Diesels tend to get complete combustion or none at all.