Basically put,
Shadowplay & ReLive are purely hardware based. Your GPU has a dedicated chip on it which is much like a CPU chip. The only thing that chip on your GPU does is encode, which in turns removes almost all of the load from your CPU and memory, apart from I/O interaction with the HDD/SSD it is writing the file to if recording, caching via memory of the data if streaming. The overhead on your CPU and GPU is minimal as a lot less communication is involved.
OBS is software based and has to rely on communicating with your CPU, GPU (Twice if using NVENC or AMD AMF encoder plugins, 1st time to grab the rendered frame, 2nd to render for output) and memory to do the same task. There is inherently more load as more communication is required to get the job done due to having to interface with all components as well as requiring the system resources to continue to produce those calls to continue the work of recording or streaming.
The difference between hardware (h264) and software encoders (x264) is hardware encoders interface with your GPU encoder, software encoders interface with your CPU to do all the encoding work. The big trade-off is you have to push significantly higher bitrate to get the same quality when using h264 encoders, for less CPU resource usage.
Probably a better way of describing the load of software recording/streaming on your PC is essentially you are playing a 2nd video game at the same time in the background.
Perhaps a dev or someone else could offer far more detailed insight to answer your question as well?
