OP, your OP is bad. You did not try honestly to get a good discussion going.
Usually these threads result in the same war between the, "Laura Croft is better now, the old games are archaic lol," crowd and the, "AAA gaming is utter trash," crowd over the same topics.
I have made my position on the controls pretty clear in the past. They are an intricate part of the game and environmental design, which is 100% designed to accommodate digital, grid-based movement that gives players impeccable precision. The controls are so precise and so repeatable that it is entirely possible to complete the game blindfolded. Others don't agree. Whatever, it's not an interesting conversation anymore.
I like both. Obviously I like the classic games better. While New Tomb Raider is a pretty expertly crafted 2015ish action adventure, with beautiful locations, exciting setpieces, tons of character drama, and all that good stuff. The games absolutely could not be easier. They could be completed by three-toed monkeys; the best content in the game is optional and hidden. The thing I like most about Old Tomb Raider is that it gave you the sense of accomplishment modern Souls players claim to like so much. When you climbed to the apex of a level, or when you finally figured out a puzzle after hours of trying everything, you just felt so good. The new games don't approach that feeling in any real capacity. There's no sense of wonder or amazement at anything other than feats of graphical splendor, and boy is there a lot of that. Completing side missions and finding X of Y cache of coins is not the same. The games are almost in different genres.
I think players of the new games interested in what the old games were like without all of the old baggage should check out Tomb Raider Anniversary. It's a brilliant game. It's a faithful remake that forges a path out on its own and eliminates any tedium, if you felt that, of the originals while preserving that adventuring spirit.
On a side note, I've sort of heard that hardcore players have used modding tools to create an endless set of expansion levels for fans to play. However, that's not really what I want-- I want a complete game with a narrative arc, a ramping difficulty, and I think I'm just not hardcore enough to do what some of these megafans can. Some new mechanics would also be interesting as well. And yes, the combat really could be improved.
I'm surprised that as all of these classic kickstarters have done so well-- indicating CLEARLY that AAA gaming is just not serving all gamers-- nobody from Core has shown up saying they want to do CAVERN SPELUNKER.
(And yes I know it's not Laura. I actually like Tomb Raider.)