My recent experience required me to change airports (LHR to LGW) to connect, then my flight was cancelled as I stepped to the desk at LGW to check in. The fact that there is NO ONE at LGW who can deal with IRROPS is a huge problem. All of the desk personnel were contractors and couldn't touch my ticket. It took over an hour to get through to someone on the phone, then several different agents before I had a semi-decent alternate plan (which, unfortunately, also included having to go back to LHR).

Even with all of its challenges, I'd pick LHR any day.