The first image is of the Black Rapid FastenR-3. It is designed to work with the other Black Rapid components, specifically the ConnectR-2 and the R-Strap. The main advantage of this type of strap is the quick movement along the R-Strap, allowing the user to grab the camera from waist height and pull it up to your eye quickly and smoothly. This is the main selling point of the Black Rapid system.
Other options to consider include the Spider Holster, which has its own unique mounting plate and strap system, while still allowing tripod use.
From your question it sounds like you are concerned with how the mount will sit on your body, and this is not only a function of which tripod mount you choose, but which strap you choose as well. More specifically, you are really comparing the different models from all different camera strap manufacturers. It isn't so much the tripod mount that matters, it is the entire design of the strap system that matters.
If you need to quickly switch between shooting handheld and shooting from a tripod, you might want a unit that is compatible with a quick release system such as a Manfrotto RC2 Quick Release Plate. If you like to carry the cameras around your waist, the Spider Holster might be your favorite choice. If you like to carry the camera(s) around your shoulder/neck then the Rapid Strap might be your unit of choice.
It really comes down to personal preferences:
- Type of photography you do
- How many bodies you carry
- How heavy are the bodies/lenses
- Shoulder/neck, Waist, back, wrist
- Do you frequently switch to a tripod
Some photographers even mix and match these systems, and find the most comfortable solution is one around the neck and one at the waist.
Overall, I think the best system is going to be determined by personal preferences and fit characteristics. Each of our bodies are different, and many of us have different camera setups, weights, and usage.
Additional Reading: Spider Holster Review