I’m assuming you’re asking about custom rigs, yes?
-Why the rigs -although slower work flow- is way better?
Custom rigs have the advantage of being specifically tailored to your needs and workflow. If you are happy with an off-the-shelf rig like CAT or Biped, this may not be as important. But most users find the off-the-shelf rigs limiting in a number of ways. With an off-the-shelf rig, you sacrifice some customization but you gain a number of tools that you would otherwise have to create for yourself.
E.g. Biped and CAT both have clip and pose management systems (including mirroring of poses), the ability to easily load mocap data, and quick auto-rigging set-ups. Getting those out of a custom rig is doable, but requires a lot more work. On the flip side, the off-the-shelf rigs also have a number of limitations or (particularly in the case of CAT) bugs.
-Can they work on the motion capture files ?
Yes, but I don’t know how easy it is to map mocap data to them. If you are also using motion builder, you should be able to map your mocap data to FBX format and then transfer it to a custom rig. I have not personally gone through that process, so I’m not sure exactly how simple or complex it is.
-Does they have a motion mixer like the one of character studio and can combine 2 different motion files to one rigg with different parts?? how about CAT?
CAT has a layer system that can in theory be used similarly to Biped’s Motion Mixer. But it is certainly not the same. With the layer system, you could sequentially blend from animation clip to animation clip, but you won’t get the same toolset that Character Studio offers. You should also be able to use animation layers–or simply loading in animation data sequentially on the same layer–to achieve similar goals with a custom rig. AFAIK, the CS Motion Mixer isn’t usable by non-Biped rigs.