This is an awesome triceps exercise that, when done correctly, also smokes the core. Using suspension straps works best for two reasons.
First, you can get a bigger range of motion. When you use a fixed bar, you're forced to do the exercise like a traditional skullcrusher where you bring your forehead to the bar. With straps, you can extend your arms forward slightly as you drop down so that at the bottom, your hands are actually behind your head. This enhances the stretch on the long head of the triceps and takes stress off the elbows.
Second, the straps allow you to rotate your hands freely as you move through the rep, making it more shoulder-friendly and increasing the contraction in your triceps.
To get the full benefit for your core, keep a straight line from your feet to your head. There will be a tendency to want to pike at the hips, so you'll need to squeeze your glutes and brace your abs to prevent that from happening. It should feel similar to the sensation you get from an ab wheel rollout. If it doesn't, you're probably not doing it right.
This is a lot tougher than it looks, so start with the straps fairly high at first (about chest level) and work your way down.