go to both, start with aleppo, check out the sites in aleppo (castle, souks, old city) and then head out and check out the surroundings of aleppo (st Simeon castle is a MUST SEE), then go to latakia and kick it on the beach (new beaches their now), then head out to palmyra and enjoy tone of the most historic city's on the face of this earth (roman, greek, persian, and muslim empire all passed through their), then head out to damascus, enjoy the night life their while also checking out the many historic sites the city holds, then take a 1.5 hour taxi ride and head out to beirut, party hard (dont listen to anyone, its as safe as you want it to be, especially for tourists), then head out to Baalbeck and check out the sites and the rich history, then go to Jeita Grotto and prepare to have your breath taken away, and if you have time head out for jordan and enjoy the many reserves they have, and head out to Jerash for some history and check out petra ( a word heritage site).....

i know i sound like a travel brochure, but its not a question of going to lebanon or syria, for a true experience you have to travel to both, and you if you are strained on time, get a good travel agent, and s/he will be able to fit all this in 7 days......