that's not really the point.
you said they should be even in 1v1. i'm not saying one should be better in all situations. there will be obvious mechanical advantages one has over another, but not all. this alone makes it impossible to have every 1v1 situation be equal without sacrificing their unique characteristics. you can't just look at raw dps either. assuming both players are perfect, sure, two weapons of equal dps will be equal. but both players wont be perfect. if two weapons of varying speed had the same dps, the faster one will win because it's less punishing to miss and puts more pressure on the enemy. if you give the slower weapon more dps, it becomes more powerful in skilled players hands, which makes the other one more useless in that level of play.
in none of these situations are things ever even. this is what i mean.
ok DPS is a bad example Imo, I don't look at guns based on their stats more or less but wholistically, their requirements for how you navigate the world and use the weapon. What you're talking about is the difference between cheap and complex mechanics - fast guns are cheap, in the sense that they are extremely forgiving but your peak performance is limited. A complex gun' like a slower firing high damage gun (it can get more complex) are hard to use but rewarding when you use them correctly.
What I'm referring to is just a general 'equality' in 1v1 scenarios with guns. Obviously a meta will always exist and some guns promote higher reward for skilled players, but theoretically, all guns should match up evenly when in the hands of perfect players. A sniper and a shotgun should be equal in a balanced map, despite the fact that the shotgun is leagues stronger in raw damage. The difference is that they have their own playstyles. Sniper has to take careful aim and keep their distance, utilizing predictive aim as well as tracking where the enemy moves out of sight. Shotgun has to Sprint from cover to cover until they enter an effective area. Both weapons have a domain in gameplay where they have the advantage, and the perfect player will seek that field so that they have the advantage. But in general, they are equal.
This is what I mean that all weapons should have an even matchup. The line for what counts as even is generally open to interpretation, but you can still get pretty darn close.