There should be no difference between the household name companies, but I once saw Royal Sun Alliance handling a death claim for a friend they were more efficient than his other insurer. However I would only choose them if their payments were cheap, since death claims are fairly conclusive.
The far bigger problem will be your completion of the health questions on the application - this is an area of wriggle room for insurers, so read the questions carefully and declare every ache and pain, just in case. They'll happily avoid paying out if you forgot to declare you smoked or had Ebola or something.
Some companies pay out on suicide and some don't.
Some (most) companies have something called terminal death benefit - where the life cover pays out early if you are diagnosed as 'definately going to die within the next year' - there are some variations in the definition of this, like some companies won't pay out in the final year - so I guess you could fine tune these final points.