Which game series is better? I'm more talking about the universes and lore

Not sure if you can really compare the two series by which is better. Sure, they both have a post apocalyptic setting, but Metro is solely a linear FPS while the Fallout series as a whole is an open world top down/third person/and first person RPG. It's like comparing Star Wars: Republic Commando with Mass Effect, while both in the same sci-fi genre, they are quite different in gameplay and mechanics

As of FO4, FO4 vs Borderlands is a better comparison where BDL wins!

GAURDian explained it well
but if I had to pick one, it would be Fallout

As @GUARDian said, its two very different games to compare.

Even in setting. Fallout has deserted America filled with retro-futuristic atributes, filled with 50's american culture, Metro, is about present time, filled with East-European\Post-Soviet\Russian atmosphere.

What by me? I found Metro (Only Metro 2033 The Last Refuge, not Last Light, not Redux Version) pretty depressing to me.

"It appears that the devastation we brought upon ourselves was complete; Heaven, Hell and Purgatory were atomized as well. So when a soul leaves the body it has nowhere to go, and must remain here, in the Metro. A harsh, but not undeserved atonement for our sins, wouldn't you agree?"

Fallout is just a really great roleplaying game and just too have goofy fun.

Metro series is just awsome because of the story and how Artyom's story grows in the 2 games. Also i really think that Metro is more of a survival and harder (In Fallout 4 you can take 500 stimpaks and in Metro just a few syringes.

Both are really great franchises and im actually hoping for more Metro games

I feel like the Fallout series has more re-playability than Metro. But the story of Artyom really makes it worth playing

Just like @GUARDian said they are both different games.

But for me, Metro wins, i love both games, but the Atmospherem lore, factions etc: is just 10x better for me, i always loved Metro and Fallout, but Metro is the game that introduced me into post apocalyptic games.

Like @"Fidller" said, fallout is a roleplaying game where you create your own character following his own story, even if you can't create a perfectly different story than other player. Metro is a more "closed" game telling a story.
For me metro is better fallout for the ambiance (the oppression of the metro) and the fact that the game is more "realist" and propose a bigger challenge in higher difficulty (ranger hardcore)

Just as a lot of people have said, the two games are both great, but different from each other. Fallout gives you the chance to really make your own story, with a character that has very personal value. Even though Fallout 4, in my opinion, removed some key RPG elements, it's still very much an RPG. Metro is a very linear, very straight forward FPS, with a little customization options. I do love it's story, and it's ambiance, it's world, but it honestly has almost no replay value for me personally. The Fallout series has always been my favorite, and even though 4 kinda seems like a step back, I still love it. The only post apocalyptic game I've played that feels kinda close to what Fallout delivers, over all, is the STALKER series.