I once had a conversation with a networking engineer from Rackspace, whose opinion was that OVS was overly complex and Linuxbridge was the right solution in most cases. That was in 2015 though, when we still used punched cards for programming.

Linuxbridge is simpler. Fewer moving parts, therefore less potential for problems and less hassle when something goes wrong. You need broader and deeper troubleshooting skills with OVS: With Linuxbridge tools like iptables and tcpdump suffice, whereas with OVS you need all of the above plus ovs-vsctl, ovs-ofctl and others. And try tracing packets that flow through an OVS bridge.

On the other hand, OVS seems to be the default, and the global knowledge base, including tutorials, documentation, bug reports etc is probably larger. Also, new networking functionality such as QoS a few years ago is often first implemented on OVS. Developers may find the richer feature set of OVS more comfortable, or perhaps they just go for the more popular solution first.

In terms of maturity, one could say that Linuxbridge has been around forever, whereas OVS is comparatively young. The Openstack Linuxbridge agent was also there first as far as I know. But OVS is used so much that it's probably as robust as Linuxbridge by now.

I have test the two methods and I found the ovs is more comfort if you need to make any further changes on your network after the installation as example in mapping physical networks with bridges or interfaces is more easier on OVS than linux-bridge cause you will map in neutron config with OVS bridge "virtual bridge" so that you can do any changes with this bridge and the physical interfaces without the neutron config takes any change