Springfield deals more damage and can reach pretty consistent two shot kills but the rate of fire is off-putting to a lot of players. Fair damage and range gives it the edge at longer ranges where true repeaters start to fall-off at. Personally I prefer the Springfield, but the Bolt Action is comfier to use and usually the safer option due to the increased rate of fire it has.
Lancaster Repeater is the most reliable of the repeaters, but for PvE it can be swapped out for the Evans for its slightly worse performance across the board but with almost twice as much ammo, allowing you to deal with large groups of enemies. Though it should be mentioned the Semi Auto is more accurate than the Mauser when using Gunslingers Choice Ability Card (they have the same/similar enough accuracy without it).
The Semi Auto has a slightly faster rate of fire, and the Mauser holds two extra shots. The Semi Auto and Mauser Pistol are pretty interchangeable. Ignoring the Volcanics as they have sort of lost their identity as the hard hitting accurate sidearm due to the Navy Revolver. While the LeMat offers a little worse rate of fire and worse accuracy, but has 3 extra shots and shotgun alt fire- a weapon with great utility. Navy is the most accurate revolver, and boasts high damage and a fair rate of fire. For the most part, Navy and LeMat revolvers are going to be the sort of high tier sidearms in the game.