I've got all the trophies/collectibles/shinies in Tomb Raider Legend.
I don't know how the other two Crystal Dynamics titles are but it felt a lot like a less polished and more linear version of the 2013 reboot
It's a game from 2006 ... and there are little grounds of comparison between it and 2013 Tomb Raider: as for the 2013 "re-boot" they rebuild the gameplay where as Legend uses most of the mechanics (the bike is new) that were established in the series and even expanded on them. Not only that, the 2006-08 trilogy* kept the tone of the old franchise, where as the "re-boot" was going in a different direction in terms of tone and atmosphere. Even the protagonist of both games only share passing similiarities, such as the name and some general features of their appearance.
* TR Legend 2006, TR Anniversary 2007 & TR Underworld 2008
That said, Legend is the low point of the three; there are still some camera and control-response issues (esspecially in Anniversay); but it is essential for the three games to work out in terms of pay-off. Anniversary will be breeze if you know the original 1996 version (the level design has been updated substantially but almost all elements of puzzle structures, progression etc are the same despite the addition of the serveal completely new mechanics - nostalgia may blind. Underworld is worth checking out if you are invested in the hooks of Ledgend (both are a story unity, with some ties to Anniversary)
In fact I mostly talked about gameplay similarities.
I replayed the reboot recently and the platforming felt almost the same if you exclude the control and camera issues in Legend, of course the shooting parts are completely different and the level design is much more linear but lowpoint or not it's still surprising that many talked about the reboot like it was something radically new for the series, yes the shooting mechanics don't rely anymore on a lock on system but that comes naturally with developers and players being used to dual analog sticks on consoles and the resurgence of the PC market.
Regarding the differences in story, I kinda took them for granted as the difference with the Sherlock-esque eccentric in Legend and the young woman who happens to just be very good at keeping her cool in dangerous situations is self-evident, though considering the similarities of the reboot with the Legend segment I mentioned it may be that they'll eventually end up similarly though I say that not having yet played ROTTR so that's only speculation on my part.
I'm not even sure if I'll ever buy the original entries, while I play videogames since the DOS era, most of my experience was with genres that were already very close to their modern version regarding controls and interface (for example PC RPGs, anything prior to Fallout and Baldur's Gate is almost unplayable to me), I've tried a demo of Tomb Raider IV and I wasn't able to get beyond the first room, they just fell very rough around the edges in terms of controls.