I haven't got any experience of using a company but can reassure you that it is much more doable than people often think. We've lived on 3 continents with our dog and we've never had a problem, even when moving (back) to the UK. We did all the paperwork ourselves, had our vet do the relevant bits, made sure we had a suitable container and off we went. It takes a few months depending on what jabs the dogs need so make sure you start the process early. There may be some things that need doing only a very short while prior to departure, too, so timeframes are critical.
It was stressful because I kept thinking, 'what on earth do we do if she gets denied boarding and we're at the airport, all our worldly possessions and children in tow? Or what if they don't let her in the other end?!!' But we double and triple checked everything and it has always been fine.
We've done UK-Latin America, then back to UK (we flew to France and then took the tunnel, as it can be tricky entering the UK directly but the route from France is well-established and v organised due to holidaymakers). Then last year we went UK-SE Asia.
The cost can be very high using relocation companies but you do get peace of mind that you won't screw up the paperwork.
The cost of doing it yourself can be very reasonable - think less than £500 for long haul flights plus the crates (v specific requirements for airlines) and vaccinations (these add up a bit but not terrible). Paperwork not expensive.
Think carefully about airlines, as not all take dogs and, of those that do, not all take larger breeds. To my knowledge, none will take flat-faced breeds in the hold. The weights they quote you are the weight of the dog PLUS the crate. In our case, this put us over the limit for some airlines and we didn't realise until after we booked a flight. Very frustrating but it wasn't clear and the customer service people are often not accustomed to dealing with live animal queries. So double check everything! We also had to hire a van to take the dog to the airport as the crate simply wouldn't fit in anyone's car, certainly not with space for any luggage or people!
If you take them yourself they go on the same flight as you and you literally wave them off at excess baggage and pick them up by the conveyer belt the other end.
You are not advised to give any sort of sedatives to the dog prior to the flight, though this always seemed sensible to me. Our dog has always been fine without. We had to fly indirectly for the Latin America trips as there were no direct routes at that time, and we were allowed to take her out of the airport at Paris for a walk. Not sure this is officially allowed but we've done it twice now.
I highly recommend Air France if they serve your location. Have heard positive things about KLM too.
Best of luck!!! People thought we were mad when we first did it (not sure what they would have thought if we'd just left the dog behind?!!) but now we've done it, we wouldn't hesitate to do it again. Probably more stressful for us than the dog!