Electromagnetic and gravitational interactions are similar - they are mediated by massless particles, they have infinite range and they diminish with $1/r^2$. The main difference is that gravity is always attractive while electromagnetic force is not.
A photon intermediating electromagnetic force has spin 1 while graviton should have spin 2. What is a reason for different spin values of photon and graviton?
As I understand it, this is because spin-2 yields forces which are only attractive, as opposed to spin-1 which can mediate forces which are attractive or repulsive. I invite the experts to weigh in on this as I would like to understand this better myself. I'll delete my answer if a more complete one is furnished.