Both are great cities with a lot to see. I think that a marathon would be much more picturesque in Istanbul. The views along the Bosphorous are gorgeous (although more so in spring and summer), and I would assume that the marathon would travel through the old city with many architectural marvels.

The food is better in Beirut, in my opinion, and the people maybe slightly better. If I had to choose only one for a leisure trip, it would be difficult. For the first-time visitor, I would see that there is more to see and do in Istanbul, though if your motivation is food and nightlife, then Beirut would be a better choice.