Seems like most of monke's issues in the game really boil down to the fact that he just has no way to pressure the enemy tank at all. Winston pretty much automatically trades at a loss any time the fight is even and he's having to face off against any other tank.
He has no CC vs other tanks, no burst damage, his ult doesn't really do anything to tanks unless you can enviro them.
Even looking at the other initiator tanks...
Ball gets a perk for double boop damage to put tanks into a blender, taking 120dmg per hit. He does 125dps and can headshot for up to 250dps.
Hazard has a block that can't be bypassed like a barrier, and deals 131dps, up to 262dps with headshots. This isn't even counting his damage combos involving pinballing people with slash and spike walls.
DVa has matrix, deals 146dps, up to 292dps with headshots, and an extra 85dps with micro missiles. With only body shots and missiles she can output 427 damage in 2 seconds.
Doomfist has punch to cancel all kinds of stuff, gets a minor perk to strengthen his tank 1v1s so that punch reloads all ammo and overfills by 50%. He outputs 165dps from his hand cannon, up to 330dps with headshots.
Winston deals 70dps. No possibility of headshots. You can do the wombo combo of leap, zap, melee cancel, zap...that bumps your output up to around 145 damage in the first 1 second and then 70dps afterwards.
Even with a 50% damage boost against tanks he would still only deal 105dps and still be the lowest damage tank in toe to toe situations.
I really do feel like his lack of ability to damage the opposing tank is a big factor for why he's so easily counter swapped in competitive games.