There are many problems with Heathrow (terminal 3). I'm sure terminals 4 and 5 are probably better. They have just announced a total refit of terminal 2.
The check in area is usually packed, as lots of people seem to bring their whole family along with them to say goodbye. However last time we flew we were late checking in with Malaysian (stuck in a traffic jam on the M25) and we just sailed through, no queues, very good service. The trick is to go through security into the departures area as soon as possible to get away from all the crowds. Once there the shops are fine and it is pretty much like any other airport.
Arriving at Heathrow (T3) can be a very depressing experience. There is usually a long cold walk to baggage reclaim, which resembles a multi storey carpark with low concrete ceilings and all the carpets are looking old and tired. The passport control hall is huge and usually packed, with long queues (but nobody there to manage them). Even if you are British you are in a queue with all the rest of the EU, last time we arrived on a Friday evening it was packed and I almost had to jostle in the queue with all the young thrusting executives back after a week working in Europe and Europeans over for a weekend in London (not easy with 2 young very tired and jetlagged children).
On the other hand, Stansted Airport is really nice. When you arrive there everything is light and spacious and new and it gives a really good impression to overseas visitors. That is what is so annoying about Heathrow, that it doesn't seem to be trying to make people feel welcome.