: They both have infinite range (1/r^2 force, 1/r potential), which implies that the quanta of both fields (photons and gravitons) are massless--and implies that there are gravitational waves (we're looking for them, but they're tough to find because gravity is weak) and electromagnetic waves (which are ubiquitous) that propagate through space at a speed c.
Differences: Gravity couples to the stress energy tensor (which mostly means mass)/ EM couples to charge. There are two varieties of charge, which an EM field will pull in opposite directions. Gravity only acts one-way. The graviton has spin of at least 2. The photon has spin 1. EM has a coupling of 1/137 to unit charges. Gravity has unit coupling to particles with planck mass. Fundamental particles have much, much less mass than this, which is why we usually say gravity is very weak