Classic Lara was an emotionally closed-off adrenaline junkie who had been disowned by her elitist aristocrat parents because she wanted to travel the globe and raid tombs rather than marry some wealthy high-society guy. She combined many admirable qualities like independence, confidence, strength, intelligence with some not-so-admirable traits and attitudes like selfishness, impatience, reclusiveness, a general disregard for the well-being of others (human or non-human) or the integrity of cultural heritage, even for her own health and safety, to form a consistent, well-rounded character.
All she cared about was the thrill of the hunt and the shiny souvenir that awaited her at the end. If she had to destroy an ancient temple, kill a few members of an endangered species and a couple of mercenaries to get that, she'd do so without giving it a second thought. Furthermore, she had very few friends and most would've probably considered her to be quite unpleasant company because she really wasn't a very friendly or outgoing person. Generally speaking, classic Lara wasn't a hero by a long shot, she was a thief, a killer and a vandal.
Now on the other hand, you have reboot Lara who studied archaeology (the actual, original Lara could not be further from a proper archaeologist) to follow in her father's footsteps, is friendly and understanding to a fault, constantly wears her heart on her sleeve and whines about her current situation and needs to reassure herself that she "can do this". They're two completely different persons and, personally, I much prefer the original. She has more depth, a lot of which is hidden beneath the surface (which only makes her more interesting - especially compared to reboot Lara who blurts out her every emotion), is more consistent in her characterisation (though, admittedly, there have been a few missteps, especially in the early games), has the less cheesy backstory and is just generally a less stereotypical and more original character.