My experiences with travelling with young ones have only been short haul experiences so far, haven’t ventured long haul with them yet.
Our eldest (now 5) took her first trip at 9 months (CE with BA) and has since travelled a further 5 times a mix of BA CE, EasyJet and Swiss business class (due to BA cancellation). Youngest (18 months) took her first flight recently with a mix Swiss business and BA CE. Both have been issue at all with no crying and really enjoyed flying (luckily).
My comparisons.
easyjet = fine but functional
BA CE = pleasant and engaging staff, very easy with T5 and good allowances
Swiss = superb and went extra mile
Swiss crew were really friendly and had little packs of colouring paper with crayons ready for the children. They gave my eldest a little bag with a toy in (I think a paper plane or something like that to make up). Youngest got a stuff teddy (Swiss plane). Staff couldn’t do enough and of course gave out plenty of of their chocolates and extra croissants for breakfast. We only flew them one way due to BA cancellation and rerouting via ZRH on outbound leg of holiday.
Lounges make a big difference when travelling with children. Definitely worth checking allowances as not all airlines are equal (BA are good here). We take our smaller stroller instead of pushchair for travel (much easier). When we’ve had to transport a car seat we have bought a big protective and then stuff it with towels or other things to pad out and protect and that has been good.
Overall, for all of BAs fault, our experience travelling with them with infants has been faultless. That being said, Swiss offer a very good experience.