It's very rare for a particular website to be cheap consistently. Essentially online TAs just source data from the GDS (centralized computer reservation system) and they typically all do it the same way. On occasion there may be "Expedia Special Deals" or whatever they're called, flagged with a yellow banner or similar. Essentially Expedia, or any online TA may buy a bulk load of seats from the airline and sell them at a discount. Other than that though there's little variation. Just buy through the airline directly.