Return and one-way are not comparable
A return fare can be cheaper than two one-way fares, but it may have a Saturday-night rule or a minimum stay. Compare the itinerary you actually need.
Baggage and seats are add-ons
A low fare may include only a cabin bag. Add checked baggage, seat selection and meals before comparing two airlines. A full-service fare can be cheaper once the extras are included.
Seasonality and the booking window
Flights around holidays and school breaks cost more. A fare observed today is a dated quote, not a promise for next month. Check the fare rules and the change fee.
Routing and arrival airport
A direct flight to a secondary airport can be cheaper but add a transfer. Compare the total journey time and the cost of getting from the airport to the final destination.
Keep the fare basis and the date
Two prices for the same route can differ because of fare class, baggage and refundability. Record the airline, route, date and what is included.