Similarities: Rip Hunter is a Time Master known for adventuring through the past and future. He also had a brief stint in a team known as The Forgotten Heroes whose main quest was initially to foil the plans of one Vandal Savage (just like the Legends).
Notable differences: Throughout the comics, Rip never took off as a mainstream hero like he's been presented on the show. Rather than the leader of the gang we see on Legends, Hunter was just a part of a team, roaming around time. He also had way snazzier ~space outfits~.
Hawkman (Carter Hall/Khufu) and Hawkgirl (Kendra Saunders/Chay-Ara)
Similarities: Carter and Kendra's story in Legends of Tomorrow follows quite closely with their comic origins. Ancient Egyptian souls, Khufu and Chay-Ara are bound together through their love for each other.
Notable Differences: In the comics, the Hawks face the ancient Egyptian priest Hath-Set, as their nemesis. Within the Legends universe, Savage's history has been mashed up with the character of Hath-Set, and the immortality of the three is intertwined.
Similarities: Vandal Savage is an immortal dickhead. The Legends version of Vandal, as we've mentioned, is actually more of a combination between the comic version and Hath-Set. But still immortal, and still a dickhead.
Notable differences: From the comics, we learned Savage's lust for world domination stems from his lengthy time on Earth as a caveman bathed in radiation from a meteorite (which gave him his immortality and enhanced intelligence).
Captain Cold (Leonard Snart)
Similarities: Fans of Arrow or The Flash will be familiar with Snart after he and his Rogues began terrorising and burgling Central City. His rocky family history and aptitude for stealing shit has translated perfectly from the page onto the small screen.
Notable differences: While Snart's persona has been pretty wonderfully adapted from his comic origins, his TV outfit is definitely lacking those "snow elf chic" touches. What, no bright yellow gun holster? No fur-lined boots? C'mon Cap.
Heat Wave (Mick Rory)
Similarities: As a pyromaniac, Mick Rory's love for fire consumes him almost to the point of pure madness. Rory relies on his co-Rogue, Snart, to bring him back from the brink more often than not.
Notable differences: Sadly, gone are the days where ol' Heat Wave was wrapped up in an asbestos boilersuit, but his lust for fiery destruction lives on! I guess he's starting fires asbestos he can.
White Canary (Sara Lance)
Similarities: Introduced into the Arrow-verse as the Black Canary, Sara went on to leave that title to her sister, joining the Legends as the White Canary. New name, new character, new outfit!
Differences: While Sara may have donned her new title, the White Canary actually only appeared briefly in the comics as a villain of the Birds of Prey, holding a deadly grudge against the Black Canary and attempting to exact her revenge.
Atom (Ray Palmer)
Similarities: Ray Palmer is the ultimate adorable nerd but more notably is also the "world's smallest super-hero" Atom! Palmer's intelligence and background in science are all true to his comic origins. His abilities, however, are slightly different.
Notable differences: Comic Atom was a research scientist who tinkered with white dwarf star matter and eventually discovered how to shrink himself to a subatomic size. The show explains Palmer's shrinkage via his A.T.O.M. exosuit that he created during his time on Arrow. The suit also enhances his strength, and lets him do neat shit like fly and shoot concentrated light beams.
Firestorm (Martin Stein)
Similarities: Stein, a Flash alum, WAS half of the duo that made Firestorm with Ronnie Raymond. Certain circumstances meant that without a new partner, the Firestorm matrix made Stein unstable, and required him to find a new match or his life would be in peril.
Notable differences: TV Stein is a pretty slick adaptation of his comic self, and there haven't been any massive changes to the character just yet!
Also Firestorm! (Jefferson Jackson)
Similarities: Initially the most reluctant of the Legends, Jefferson Jackson's major similarity between the comics and his TV counterpart is that he was a football star in both. Thaaaat's about it tbh.
Notable differences: Fans of the Firestorm comics may recognise Jefferson as Ronnie Raymond's best friend. He was a supporting character in the comics who never actually became associated with the Firestorm matrix. The show moved Jackson from Ronnie's BFF to his replacement after events in The Flash caused Stein to require a new pal.