What are the differences between Deadlands: Doomtown and Doomtown: Reloaded?
Both games are indeed similar. They are both set in the Deadlands universe (although Doomtown: Reloaded does not explicitly say it, despite there being obvious signs such as Harrowed, Hucksters, and other references to the setting). Both have the basic mechanics of cards having playing card values and the need to control locations while managing ghost rock. And both have an ongoing story that is in continuity with the other.

The big difference between the two is that Deadlands: Doomtown was packaged as a collectible card game. Doomtown: Reloaded on the other hand is what AEG calls an "Expandable Card Game", which is exactly the same as a Fantasy Flight Games' "Living Card Game" (Fantasy Flight Games trademarked the term, so AEG had to come up with something different). Instead of having booster packs, new sets have 4 copies of every card in them, so you don't need to scour for that one card you need.

As for actual rules differences, the core gameplay is the same, but there are a number of important differences. A fanmade compilation of the rules differences is pretty exhaustive. A few highlights:


  
  Decks can only have 4 cards of the same suit and value.
  Dude and deed Uniqueness only applies to your own gang.  Different crews can have the same dude or deed in play.
  If you equip more than one weapon or horse the previous weapon or steed are discarded.
  Skills checks are now equal to or greater, instead of just greater than the target number.
  Aced dudes no longer have their gear sent to boot hill.  It is discarded instead.
  When resolving shootouts, a dude can be discarded for 1 rank difference in casualties, and aced for 2 rank difference.  If they are harrowed, they can be sent home booted for 1 rank difference, discarded for 2 and aced for 3.
  Bounties can be increased beyond 1 ghost rock, and anybody with a bounty is considered wanted (if the amount is reduced to 0, they are no longer wanted)
  Law Dogs (or any other faction) are no longer able to boot to remove bounty
  Card memory no longer exists (i.e. once a card is out of play, all effects on it, including permanent effects, are removed and not added back if the card is returned to play)
  The player with the most influence no longer draws an extra card at Nightfall (now called Sundown)
  Fear level no longer exists
  Events no longer exist.
  


There are also a number of new mechanics, such as Grifters, which allow you to activate their ability at the start of the game if they are in your starting posse. For instance, the Grifter in the base set can boot to shuffle your starting hand into your deck and draw 5 more cards (this ability can only be used once at the start of the game).

You may also notice that there are some general paradigm shifts in Doomtown: Reloaded. For instance, a developer diary explained that it was intentional that there are so few Out of Town locations (basically, the Out of Town "landslide" deck that was used often in Deadlands: Doomtown became too powerful and too difficult to contest, since movement was restricted). 

Despite the similarities, the two card sets are not intended to be played with each other and the tournament rules explicitly state that you cannot use Deadlands: Doomtown cards with Doomtown: Reloaded. That said, it probably is possible to mix them, so long as you remove any cards that contradict with any new rules.