Since no one else chimed in on the comparison I guess I'll give a generic answer based on generic hull shapes for what it is worth. I have not been in either boat and I don't have access to the hull spec details. This is just based on what I have studied about hull designs.
The R23 appears to maintain much of the larger tugs hull design. It leans more towards the semi-displacement hull than the C-24. This means it has a slightly flatter bottom at the stern requiring less horse power to climb to a "semi" plane but limits it's rough water capability at higher speeds. It also has a more vertical stem giving it a relatively longer waterline length to its overall length. This may give it a slightly higher hull speed and thus improved efficiency and tracking at displacement speeds. The waterline length also increases the available volume inside. In short, it should be more efficient for the volume, cost and weight but has a reduced top speed and handling at that speed. It also is designed this way to look more like a tug.
The C24 hull is shifted more toward a deep V planing hull. This should provide better rough water performance at higher speeds at the expense of more horsepower to get up on a plane. The raked stem should give it better handling at higher speeds as well but trades off the performance at displacement speeds and volume inside the boat. In short, it is focused at higher speeds and handling at those speeds but needs more HP and a bit less volume (relative to overall length) to do it. This form also gives it a different look (not a tug look).
The bottom line is a matter of speed, HP required, style, and volume in the boat. Both are great boats but are focused on different priorities.
Hope this helps.