The demo features the Avenger and Predator Pistol in the intro level. The second level has the Mattock, Predator, Tempest, and Eviscerator. You can't access the loadout menu nor the weapon customization bench in the demo.
Avenger now has 30 shots per thermal clip and shoots slower, but seems to be more powerful now. It also sounds more like a sci-fi rifle than the Avenger in ME2.
Eviscerator sounds really beefy this time. It also has significant range now.
Mattock's firerate has been capped, a quick trigger finger can reach the maximum cap without Adrenaline Rush.
Predator has increased capacity from 12 to 15, and can fire as fast as the new Mattock now, maybe faster. The sound also has more punch this time.
Tempest sounds somewhat silenced, but still sounds nice unlike the Locust from Kasumi's Loyalty mission.