Hi...we are 40 yr old expats from NZ and have been travelling back to NZ every couple of months. I have always had an airline seat for my son since he was 5months old, and have never used a carseat on the aircraft - he is now 2 3/4years.
We use a limo or taxi to the airport, I never used a carseat, but the companies do have them to rent if you order it in advance - I don't know the cost. Since you have a carseat organized for the UK it is rather cumbersome to take your Britax when you have all the other "essentials" for entertaining him. Personally I wouldn't take it, because he is going to want to sit/climb/play on you alot of the time. Having the airline seat is great for when they sleep - definitely gives you extra room. I know AA/UA don't offer infant seatbelts as on Qantas/Air NZ, you will probably hold him for take-off as he may not want to sit in the seat alone - apparently you can buy fly-safe seatbelts for infants, I've never used them though - when we travel on the US airlines I generally held him without a belt for take-off.
I always use an umbrella stroller - something you don't mind getting beaten-up abit. They don't always let you take it onboard. When you're tired some of the airports have a long walk - and all of a sudden he's very heavy.
You probably have it worked out...but take enough diapers, and an extra set of clothes for the little guy...spills happen when you least expect it!, and some toys/books and favourite toy!
If you do decide to take the seat...you can buy a trolley which clips on to your carseat - they're about $90 I think. They fit most carseats, this way it is a stroller/carseat too. The Right Start on Clybourn has them, and I'm sure other stores do too.
We have to take two flights to get down to NZ, so have been disrupted a couple of times - thankfully I had extra diapers for the trip!
If you need any other info let me know.
Caroline