Does theoretical physics suggest that gravity is the exchange of gravitons or deformation/bending of spacetime?
General relativity describes gravity as curvature of spacetime, and general relativity is an extremely successful theory. Its correct predictions about gravitational waves, as verified directly by LIGO, are especially severe tests.
Gravity also has to be quantum-mechanical, because all the other forces of nature are quantum-mechanical, and when you try to couple a classical (i.e., non-quantum-mechanical) system to a quantum-mechanical one, it doesn't work. See Carlip and Adelman for a discussion of this.
So we know that gravity has to be described both as curvature of spacetime and as the exchange of gravitons. That's not inherently a contradiction. We do similar things with the other forces. We just haven't been able to make it work for gravity.
Carlip, "Is Quantum Gravity Necessary?," http://arxiv.org/abs/0803.3456
Adelman, "The Necessity of Quantizing Gravity," http://arxiv.org/abs/1510.07195
Gravity is as simple a force as all the others, which means that its simple when not looked at too closely, and far more sophisticated when it is. Given that it’s generally supposed all forces are merely low energy relics of a single high energy one, we might suppose that all the forces are as complicated as each other when looked at closely.
Popularly, Gravity is seen as different from the other forces in that its geometric. It turns out that the other forces are also geometric. Nevertheless, the main difference is that in gravity, the metric tensor, which tells us how to measure distances, times and angles is directly implicated in a way that it isn’t in the other forces. For example, there are two equations in EM, one of which does not involve the metric and hence seen as topological, and the other, which does (via the Hodge star) and hence, is coupled with gravity. The other two forces, the weak and strong force are modelled as gauge theories of the Yang-Mills type and hence directly generalising the EM equations. So similarly, they also have a topological and metric aspect, and the latter means it couples to gravity.
Now, whilst gravity hasn’t yet been quantised with several ongoing major projects that attempt this there are several partial semi-classical results which are used to help orientate research into this. One such result is that the quanta of gravity, the graviton, is a massless spin-2 particle. This is understood by looking at a linearisation of gravity which is used in the theory of gravitational radiation, and then by quantising this to show we have a massless spin-2 particle, aka the graviton.