The second installment of X:COM series is, basically, X:Com Enemy Unknown with game-breaking design flaws straightened out for much better replay value. The one real problem of the original X-Com was that a player who already knew the research three could jump to endgame technology in just few months, then turn the tactical part into point and click slaughter, delivered by mind controlling soldiers in flying suits, armed with automatic heavy plasmas of doom and guided blaster missiles. TftD goes to great lengths to re-balance the game and keep it challenging until end stage; more complicated research tree stops player from getting endgame tech and mind control early on, surface missions stop some game-breaking equipment from working and the most powerful guns are semi automatic option. Along with more challenging aliens it forces player to stick to squad level tactics (with emphasis on concentration of fire and mutual support) to the very end, rather than coordinating invincible exterminators. If you start X-Com series with this one rather than Enemy Unknown, the original game will always feel simplistic .
The changes to the story, artwork style and atmosphere - which was very generic in original - may be a welcome change, too, depending on your tastes.