Whether you should book direct with the airline or through a third-party site is the wrong first question. The price you see on a booking site is almost always a real price. The thing that actually differs isn't the number. It's who owns your reservation when something goes wrong, and that only matters on the small share of trips where something does.
When the middleman is fine
Most flights are uneventful. You show up, you fly, nobody's plans change. On a trip like that, a third-party site that shows a lower total is showing you a genuine saving, and taking it is the sensible move. The ticket is the same seat on the same plane either way.
Where the booking site earns its cut is breadth. It can put two airlines that don't sell tickets together on one itinerary, or surface a fare the carrier buries three screens deep. That's real value, and it's most of why these sites exist.
When you want the airline's phone number
The trouble starts when the plan changes, and it's rarely your plan that changes first. A schedule shifts. A leg gets cancelled. You need to move a date. Now the question is who can actually touch your reservation.
Book direct and the airline owns the whole thing. It can rebook you, refund you, or wave you onto the next flight without asking anyone's permission. Book through a third party and the airline often points you back to the site, the site points you back to the airline, and you spend an afternoon being handed between two support queues that each think the other should fix it.
This is also where the 24-hour cancellation rule gets slippery. On a U.S. itinerary the free-cancel window is supposed to follow the ticket, but plenty of booking sites layer their own service fees or their own rules on top, and a "cheaper" fare that quietly drops that protection isn't actually cheaper. It's one more line in the gap between the sticker price and what you really pay.
What we do, and don't
We don't book anything for you, and we don't push you toward the channel that pays us, because we don't take a cut of where you buy. We show you the real fares and leave the booking to you. Our only advice is boring and holds up: if the trip has any moving parts, if the dates might shift or a connection is tight, the airline's own site is worth a few dollars for the shorter phone call later. If it's a clean round trip you'd never need to change, book the cheaper one and don't think twice.