The differences between Black and White are as follows:
Black version exclusive Pokemon:
Weedle, Kakuna, Beedrill, Murkrow, Houndour, Houndoom, Shroomish, Breloom, Plusle, Volbeat, Honchkrow, Cottonee, Whimsicott, Gothita, Gothorita, Gothitelle, Vullaby, Mandibuzz, Tornadus, Reshiram
White version exclusive Pokemon:
Caterpie, Medapod, Butterfree, Paras, Parasect, Misdreavus, Poochyena, Mightyena, Minun, Illumise, Mismagius, Petilil, Lilligant, Solosis, Duosion, Reuniclus, Rufflet, Braviary, Thundurus, Zekrom
Pokemon Black has Black City, where you can get more items and battle high leveled trainers.
Pokemon White has White Forest, where there are many Pokemon exclusive to White from past games, these Pokemon are:
Pidget, Nidoran male, Nidoran female, Oddish, Abra, Machop, Bellsprout, Magnemite, Gastly, Rhyhorn, Porygon, Togepi, Mareep, Hoppip, Wooper, Elekid, Magby, Wurmple, Lotad, Seedot, Ralts, Surskit, Slakoth, Whismur, Azurill, Aron, Trapinch, Corphish, Bagon, Starly, Shinx, Budew, Happiny
Pokemon Black and White both have different gym leaders in the final gym city, Opelucid City, but they have the same team. In Pokemon Black, Opelucid is more futuristic, while in White it is more rural.