One that comes to my mind is Fallout New Vegas.
The starting 556 bolt action rifle to the carbine to the LMG or marksman mine. All use the same ammo, deal similar damage but RoF, range and other proprieties affect how great it is. FNV also has different ammo types. You can use slugs in your shotgun. You can use dragon breath. If an enemy is distant and has significant armor, buckshot wouldn't be as effective as slugs.
Other example is VtMB. Your starting .38 special revolver is trash. Not against humans but against supernatural foes. When you unlock the .44 Magnum revolver, it becomes very effective against supernatural foes.
In Warsword Conquest mod for M&B, there are different types of firearms, near all firearms are fire and very long reload. But there are some advanced weapons, you can buy an double barrel pistol in altdorf and some rare merchants have repeaters but they are expensive as hell. One game will play toghether with a group is Savage Worlds : Deadlands. I was seeking a OSR group but found a group for it and will play this weekend my first section. The game not only features guns but also has single action revolvers and double action revolvers, as well precursion revolvers who requires powder, precursion caps and very slow reload
It is fantasy wild west. So the focus on guns is much more expected than in a game where it is a novelty. The art is gorgeous.
Other game that features guns is UnderRail.
Snipers if crits hits like a truck.
Sidearms, are available in all types of cartridges, an .44 handgun is devastating but ammo is expensive and requires too much AP. An lighter gun is the opposite. There is no better gun, just situational gun.