AFAIK
The dedicated Civil SAR S61Ns have the SN450 digital autopilot, which outperforms the Mk??? AP in the SK 2/3/4/5/6/7. The SK3A has the SN500, which does essentially the same as the 450;probably has a few more megs of processing or something to justify the extra 11.1* %. I believe all except the Mk4 are regulated to allow zero vis approaches to the sea surface, and if you took the gags off the Mk4 AP buttons and gave the crews appropriate trg they could do it too (though clearing the space for descent without a radar would be 'interesting'). So to suggest that one or the other (mk4 excepted) is better in IFR terms is a dodgy argument.
The 322Ls probably have something newer and better.
The Merlin AP has similar capabilities to the 450/500 (with better duplex protection?? - Merlin drivers help me here) except that its autohover / hovertrim is inch-perfect and has the potential to change SAR SOPs a lot if it were to come into service. This may already be happening with the three EH101 variants already in dedicated SAR service worldwide.
Nose mounted radar has some obvious advantages (see where you're going, pilots have the picture directly available).
It also has numerous disadvantages (no north stab / ground stab hence no map overlay, can't see behind you - handy when reversing to the coast in an onshore wind, distracts the NHP from looking for visual references, much smaller coverage for a search).
I would not like to have to give an overall superior rating to one or the other.
Considering the original question.
There is a spectrum of operational experience available in UK SAR which the BH crews are unlikely to run across routinely. All-weather ship ops explore much of that spectrum - hence the RN view that UK SAR is a "respite tour". It is highly desirable that the BH force have a chunk of that experience embedded (you never know what you might be asked to do on deployed ops). Therefore the concept of mil involvement in UK SAR has some merit.
However, to do UK (or anywhere specific) SAR to the highest standard requires local experience and expertise. This is mostly gained by having been there and done that. Civilian crews, who (correct me if I'm wrong) generally treat the job as an absolute end rather than one step in a career progression, may over time gain an advantage in this respect.
So the answer is:
From the military point of view, yes.
From the national point of view, maybe - there are conflicting priorities.
Sven