[With any site] Find who has the most direct method of travel. Book directly through end-provider site
[With preferred hotel network] Find which hotels are in network and near where I need to be. Book directly through end-provider site.
Service directly though the end provider has been much better overall (IMO) when there is a problem. I don't use AirBnB or similar as the last thing I want is shitty human reps I've had to deal with in the past. In rewards-network bookings tend to drop 10% or so vs list prices, with some fees waved so prices haven't been a decided factor to use a 3rd party.
Won't do Spirit/low cost flying unless it's an overnight thing though and only need a backpack.
^ for when I get to decide. If it's paid for as part of a contract I'm slightly more flexible. Business travel has had more flexibility on cost so can also swing some extra benefits like traveling by train instead of flying.