I would like it to be made old school and fast paced. I honestly think Turok: Dinosaurs Hunter's "The Hub Ruins" area and how it is used as a base to the game is actually a perfect way to go, on how the game should be except the hub could be much bigger and more to explore and you could upgrade and travel here. Then the portals could be the levels. I would like to see a new version like Shadow Warrior 13 except more exploration.
This is on my old pc 
But I like the sword fighting and I imagine Tal'sets Warclub acting like this. Plus you know there are other weapons to as seen and you can upgrade them a bit. I think this with much more exploration in jungles/temples fighting other tribes and dinos would be perfectly okay.
I will certainly keep the hub structure of Dinosaur Hunter but with the more organic level design of both Turok 3 and Evolution.
The first level could easily be the jungle with the enemies being the Dinosoid army, regular dinos, and wild prehistoric animals like saber tooth tigers, dire wolves, ancient hyenas, among others. The following levels will have their own themes, with the dinos always making a return but with some differences. For instance, if one level is a catacomb or ancient temple teeming with evil tribesmen and evil witch doctors then you could have undead raptors that were reanimated by their magic. Or if in one level you are in a swamp or bog teeming with a new enemy type then dinos could be mostly aquatic based; raptors could have amphibian characteristics, leaper colonies could have a more dominant presence in certain parts, and the more intelligent ones like the Endtrails could have different equipment. The final level would be the futuristic-type, but maybe give it a more steampunk vibe to it much like Evolution handled technology.
In terms of weapons, I will return the weapon wheel with a total of 16 slots much like Turok 2. Each one will have either a secondary mode or function via a upgrade. For instance the shotgun can use both regular and explosive shells, the minigun could transform into other weapon as it's secondary function ala' Evolution, maybe the Pulse Rifle will have a secondary function that will act as the Alien Weapon from Dinosaur Hunter among others. I would certainly return the Cerebral Bore that's for sure.