Hello Heathrow Director,
I suspect that sometimes the differing avoid headings are because the same piece of weather 'looks' different from different angles. Sometimes the heading is also based on what you can or can't 'see' beyond the first piece of weather.
Penetration height also makes a difference - are you in the rain/hail/lightning strike likely height.
I am also much more conservative if the cabin crew are still out of their seats.
Aircraft have different rides in turbulence.
Examples might be - the A320 is different to the A321 and they are different to the B757 and all of these are different to the B747. Crews will make comfort decisions based on their experience, rules, company culture.
It's a while since I flew in/out of LHR so I don't know if you still don't have a wx radar display available to you. I do remember experiencing a number of days in a previous existence when the whole LHR arrival and departure flows were trashed by the controller being unable to see the weather we were all trying to find a way round/through. Equally, I remember being one of three aircraft being refused avoiding action at LHR due to parallel queues on right base. My aircraft just got a good thumping, but both the others ahead of me got multiple lightning strikes and one had the radome opened up by it. I can't help contrasting that with ORD and SIN to mention just two vastly different airports that provide the controllers with good weather info and so they handle wx quite elegantly, flexing departure and arrival routes. The habit of co-operation between controllers and pilots there is well established and trusted.
I am sure that, with the pressure of flow rates that you guys work under, it is frustrating to see a carefully shoe-horned plan get chewed up by us wandering around.
What can you do to help us, and what can we do to help you?