Of the two only the steadicam is designed to get the kind of smooth walking shot you mentioned - however, they take some time to balance correctly and then you also need practice with it because it's really a skill to know how to use one.
The shoulder rig is much easier, I'd worry about the quality of the one you linked to being that it is so inexpensive and looks like it is mostly plastic.
I think it depends largely on you. Both act to stabilize footage, but not the same way. The shoulder rig has far less of a learning curve since it just needs to rest on your shoulders and it stabilizes by balancing movement among your hands and shoulders. The "Steadicam-pole" thing relies on your hand to stay stable while balancing the weight out with counterweights. I find these rigs get heavy fast and you can only shoot for short periods of time - all the while your hand and shoulder drop due to constant weight and motion. At the end of the day, you will need to stabilize the footage in post anyway (whether Steadicam or not). I suggest the shoulder rig for less overall strain and ease of use. For long term shooting, the shoulder rig will work quite well. I would skip the handle stabilizer rig and rent a better unit that attaches to your core like a real Steadicam for the correct feel to the footage. Another note: steadicams wobble and pivot and take a bit to fully stabilize with weights and such and take much longer to get used to - learning curve with steadicams.