Simplified: none of the two :)
First you should identify the real bottleneck:
1) Switch LANa to router
2) Router interface outgoing to LANb
3) Switch LANb to router
4) Router interface outgoing to LANa
In case 1) or 3) is the bottleneck - look for drops on switch interfaces - the problem is best addressed in the switches. And there queueing should solve your problems.
In case this is not possible or 2) or 4) are the case, imho CBWFQ (Class Based Weighted Fair Queueing) would do the job.
Traffic shaping will always throttle the traffic of host A to the configured rate ... even if no other traffic is present. This is achieved through queueing.
Policing will always restrict host A to the configured bandwidth ... even if no other traffic is present. This is achieved through dropping packets.
Queueing however will only restrict A in case there is more load on the interface than it can handle. In a sense it protects one class from another.
So to get the most out of your network I would choose CBWFQ.
regards
Martin