You simply cannot (reasonably) use the subnets 192.168.255.0/24 and 192.168.0.0/16 in the same network since they overlap.
Using them in separate L2 segments makes communication between them impossible (without trickery).
Using them in the same L2 segment enables normal communication inside the overlapped scope 192.168.255.0/24 but 192.168.255.0/24 nodes would require a gateway for the rest of 192.168.0.0/16, even if they are within direct L2 reach.
The broadcasts overlap as well, as you wrote. Note that directed broadcasts are translated into L2 broadcasts once they reach the destination subnet (they can be routed, depending on configuration). The L2 broadcast is transmitted to all nodes, 192.168.255.0/24 and 192.168.0.0/16 alike. Both subnets' nodes also match the destination address to their directed broadcast address, so they'd all process the packet.
This is all no good practice at all. Overlapping subnets generally cause routing conflicts and must be avoided.
192.168.0.0/16 can be used as an aggregated route where appropriate but don't overlap subnets of any size.