I mean, to be honest, there isn't much else we can do to differentiate the past and the future other than textures and models... Because of the seamless time travel mechanic, we can't have different level geometry, because otherwise the player would easily get stuck when time travelling - there are already a few instances where this happens, actually. We had plans to have an additional enemy type for the future that had to be cut due to time constraints, but other than that, I can't really see how else we could have differentiated these timelines on a jam build.
When it comes to the weapons, I still don't really get what you mean... All the weapons play differently except for two, the two automatic ones, and still, their only difference isn't just "being from a different time period", they have different proficiencies against different enemy types. The reason why you would choose between weapon A or B is the enemy you're currently fighting. The MP40 is twice as better against future enemies, and the Laser Rifle is twice as better against past enemies, to encourage weapon switching while also having a fast-firing stagger weapon for both situations. It's kinda like Doom, you can play through the whole thing with just one weapon and it will feel samey, because that's not the optimal way of fighting.
M1 Garand is your safety net and you'd only ever use it when you're out of ammo, MP40 and Laser Rifle are the auto stagger weapons, the shotgun is devastating at point blank range (especially against future enemies) and has less spread when aiming down sights, the rocket launcher is a AOE weapon with blast damage, and the railgun is a guaranteed one-hit kill to all enemies except the strongest one, with infinite penetration.
Also, you can shotgun jump with the shotgun! We don't explain that because it's a fun mechanic to discover (and you can also pretty easily boundary break with it), but it's there. The Railgun also has this effect, but its knockback works on any direction, so you can even use it to cheese the platform puzzle.