Well the first apartment looks a little better decorated etc. but it is in a very busy, noisy and touristy place. The second apartment is in one of my favourite parts of Florence (I stayed on that very street last year). It is much quieter, with fewer tourists, more locals, decent restaurants, nice wine bars. So based on location alone, I would go for the second one.
Thank you. We do want to avoid busy places, but still be close to the main sights for our first trip to Florence.
I have one more. Is this also in a very busy area?
Not quite as bad as staying where the actual market is, but it is the same area as the first one you were considering. I have also stayed on this street and found it very noisy at night from the street cleaning machines. Mind you our apartment faced out onto the street, if this one is in the back, then it probably wouldn't be so much of a problem.