They're planning throwing away most of the first stage and catching the expensive engines on parachutes in mid air with a helicopter above the ocean then landing them on a barge softly enough not to damage them. They haven't actually done this or even built the engines to do it. They have represented this purely hypothetical approach as more efficient than reusing the entire first stage, because you sacrifice less payload weight and they claim refurb costs will be higher for full reuse. In practice if you can deliver whatever payload the customer wants they don't care how you do it, and of course refurb costs are likely to be almost entirely down to engine refurb, which they'll still need.
It's certainly not obviously more efficient or quicker reuse, it's likely to be slower and far more costly if they actually do manage it, so saying it is more efficient is just a way for ULA to try to sound like they are still a contender, even out their launches are still significantly more expensive and they haven't even tried to reuse engines.
Not to mention the complexity inherent in getting the engines separated from the rest of the vehicle.
Also, they're at totally different places along the technological readiness curve. They're proposing a theoretical concept, SpaceX has already recovered two first stages. Even if their parachute concept was theoretically superior (which I don't think it is) by the time they got it working, SpaceX would have years of operational experience with hoverslam.