I graduated from Sackler but I interviewed and was accepted at both programs.
Both are excellent programs to learn academic and clinical medicine. I don't know that much about BGU but I would say they're about the same as far as training. Both programs get good residencies in the United States, but neither of them is as good as a US school as far as residency placement.
BGU offers a richer cultural experience, because you're out in the boonies and not in downtown Tel Aviv. However, being in Tel Aviv is pretty nice because TA is an incredible city, whereas BGU is in the middle of the desert.
Reputation: Sackler has been around 28 years, BGU 5. People just know Sackler better, so that leads to a stronger reputation. Also more alumni out there to help you. However, BGU's affiliation with Columbia helps a lot.
Tuition: BGU unfortunately costs more because they only offer private loans (unless they've gotten that figured out). Government loans are way better than privates.
I chose Sackler because it's in the city, because it has a stronger reputation and they offer government loans, but I could have easily gone to BGU and probably have been happy.