I've been to both a few times. I think the Club lounge is great at LGW but prefer the First lounge as:
- table service / food to order is pretty good: I like the BA burger before a flight
- better drink offering: nice champagne on free-pour
- quieter: always pretty quiet in my experience which at peak times is definitely not the case in the Club lounge...also, because it's predominantly GCH/OWE rather than true 'First Class' there are very few people in there for whom the lounge is a novelty or treat: so people (by and large) behave a bit more normally...whereas in Club I've been subjected a few times to the stag/hen do type groups attempting to drink the bar dry, the guy making several phone calls basically just to tell people he's "in the lounge" (yawn) etc etc., the people tutting at the mere thought of my (very quiet, well-behaved) toddler being in the lounge at all - I will get flamed for this but at least in the Flounge everyone is a frequent flyer and by and large is a bit more normal about the whole thing