Returning to Wolfenstein('s Roots)
It's hard to recommend the 2009 Wolfenstein "reboot". In fact, based on the lackluster story and strange, supernatural gameplay of that game, it shouldn't be expected that Wolfenstein: The New Order would improve on the series. However, it does so in nearly every way.
The great thing about the old Wolfenstein and Doom shooters was the ability to just run-and-gun your way to wrecking everything and everyone in front of you. This is mostly returned in The New Order. Sure, you can aim down the sights. But The New Order allows you to just dual wield assault rifles, pistols, and automatic shotguns and plow through Nazis like they aren't even there.
In regards to the stealth option, it's very difficult to really stick with that type of approach. There are several places that the game pretty much funnels you into a stealth situation, hinting through the enemy movements and lack of weapons that you should be doing it. In most of the other spaces, though, the game is much more linear, requiring you to gun down everything you see. The game often switched between these two modes, but never does it feel like one path can be taken for the whole game, like 2012's Dishonored.
The AI can be dumb in places. Often, when spotting you in stealthy sections, they will say "Huh?", maybe look in your direction, and then go right back to their routes. I encountered this in all difficulties. However, in combat, they are pretty intelligent. They will take cover or rush you with a knife, making them tough but not impossible to take down. They aren't bullet sponges, making combat non-frustrating.
The story is better than it should be. It is a very serviceable and interesting take on post-World War II, and it allows them to implement all of the mechanical and engineering marvels they wanted. The writers seemed to work very hard on crafting a portrait of Blazkowicz instead of making him just "the guy shooting Nazis". Is it deep on the level of Bioshock? No, but for a Nazi-killing gore-fest, it works.
Overall, The New Order is not a game you should miss. It is a great game no matter the platform you play it on. It really leaves an encouraging feeling for what Machine Games will do next, especially if given the ability to build their own game from the ground up.