We are in the mid-west (sort of) and have no direct flights from our local airport to the UK, and I am worried about our cats being transferred to the right planes and if anyone will come and check on them or water them between flights. Esp because we are looking at flying during a time of year that is still typically warm here. If I book it myself, and then flights are cancelled because of the heat, then I would be stuck trying to scramble to reschedule them. I would hope that a Pet Relocation Agent would be able to get them rescheduled again quite easily.
I flew my cat (domestic) from NC->NM in November, so there were both temperature concerns to deal with (if there were especially hot/cold weather in NC, Dallas where her layover was, or NM). I had to get a vet's signature saying she was acclimated to a certain (minimum) temperature, and that was it. Granted, I booked her flight about a week in advance, so not as far out as is allowed for international flights, but it should be fairly reasonable to have an idea of what temperatures will be when the flight goes. The airline was quite helpful with that as well.
During her layover in Dallas (approx. 2 hours) she was checked on (not taken out of her crate) and given water. I sent her along with food as well (per airline advice), in case something really weird happened and she had a longer layover. She arrived safe and sound, and the airline folks took quite good care of her. (This was also with the complication of having one person drop her off and another person pick her up, so there was extra coordination involved, which they handled quite well.)
It's up to the individual what they want to spend, but I spent about 5x as much moving my pets as myself. I don't think I would've spent any more, even though I could've afforded it. I love my boys, but I was willing to do the legwork myself to get them over here rather than pay even more for an agent's help.