Openvswitch is a sophisticated switch that can be controlled using Openflow and permits managing traffic that flows through it in many ways. Linuxbridge is the default switch implementation in the Linux kernel and can be compared to a simp,e hardware switch like the ones we use for home networking.

Linuxbridge is simpler, therefore simpler to troubleshoot. Openvswitch offers more features, though I am not aware of a list (and such a list would depend on the particular Neutron release). Both are mature technologies. It depends on your use case which is better.