If the sides have a permanent voltage relationship, for example V1 > V2 always holds, then the two-switch topology is simpler and H bridge offers no advantages.
Two-switch configuration is equal to synchronous buck and synchronous boost, depending on the direction you look it from. With a H bridge, you can arbitrarily choose which side bucks and which boosts, so both V1 > V2 and V1 < V2 become possible.
If I understood you correctly, the advantage of an h-bridge is that continuous conduction mode can be maintained at all current levels, just like with any synchronous switch converter.
No, continuous conduction can be maintained with synchronous half-bridge, too. The key to forced CCM is use two active switches instead a switch + diode, this is enough.
H bridge allows these configurations:
V1 > V2, current flow 1 -> 2
V1 > V2, current flow 1 <- 2
V1 < V2, current flow 1 -> 2
V1 < V2, current flow 1 <- 2
Half bridge only allows the first two (or latter two, depending on which way you define the labels).