This was a classic case of an inter-agency rescue. An "exercise" had been conducted a few weeks earlier that (luckily) had quite a lot of commonality with the actual incident. In this case, there were two Sikorskys on scene and they would have had space for 30 POB between them.
The RNLI and Coastguard Helo service are not competitive but rather complimentary. Here the CG will often deploy both, but generally one service has an obvious advantage on scene. It's not always clear in advance which it will be.
When it's a straight race to a sinking vessel offshore, then the helo will often "win", but it can be slow to deploy and incidents are often far from the base. An RNLI RIB/new Offshore in a forward position can be on the water and doing 30/25kts in under 10 minutes. Helos are crap under cliffs and can't handle large numbers of PAX quickly. In addition, the helo crews are often flying into relatively unknown (to them) territory, wheras the RNLI crews know every point and bay on their patch. Comms from the CG are skewed to a "land" perspective and without co-ordinates, an aircrew can find their "instructions" difficult to interpret into useful data.
BTW, I had a guessing game with a WAFI today:
willk "how many casualties can a Tyne class hold?"