I did it directly with KLM - never had to deal with a pet relocator in North America, just followed the paperwork requirements.

Direct may be best for your pet. I like KLM because they were checked by a qualified vet, had their cages cleaned, were watered, walked (or litter boxed) mid way through their journey.

It's your call and your pet. I can't say if one is better than the other, but I was happy with my trips (4 total) although I can't vouch for my pets :-