My normal advice is to burn the miles on First provided that those miles would not have been used to cause you to travel in Club instead of a lower cabin on a flight in the future.

Some more detailed analysis:

Check-in and bag drop: no tangible difference

Fast track security: no difference

Lounge: the Concorde Room has a more pleasant ambiance than the Galleries Club but although the Concorde Room's food is different, based on limited experience I am not convinced that it is actually better - if you like wine and champagne the Concorde Room is probably better, but for spirits and soft drinks the two lounge classes are almost identical

Boarding: no difference

Seat: the First seat is much more spacious than the Club seat and I find First a much more pleasant place to spend a flight than Club - the larger table and side space in First allows me to do serious work whereas the more limited space in Club limits work to trivial matters

Sleep: I find that I sleep slightly better in First than Club - a Club seat allows me to operate effectively the next day but a First seat gives me the evening as well

Catering: You will get a good meal in both First and Club, but I really like dine-on-demand in First as it gives me the flexibility to do other things like watch a movie or read a book before having to worry about interruptions due to the service - First has slightly better alcohol with Club and I really enjoy the sweet pudding wine.