Momondo is a travel fare aggregator that searches many different smaller travel agencies to get you the best price. Momondo is actually owned by Priceline and Kayak.com, who paid $550 million to acquire Momondo in 2017.
For most international flight deals, I find that I can save $30-50 by searching with via Momondo and booking with a smaller travel agency. However, you need to weigh the pros and cons:
24 Hour Cancellation- If you purchase a flight departing the U.S., you can cancel within 24 hours. Travel agencies, with the exception of Priceline, likely charge a fee ($20-50) to cancel a reservation.
Less Customer Support- Smaller agencies can offer better deals when they have smaller customer service teams. Therefore, if there are any issues with your booking, you may find it harder to get in touch with a customer service representative.
American Express Platinum- The Platinum card offers 5x membership rewards points when you book directly with an airline. Booking with a travel agency would only net you 1x points. Other cards, such as the Chase Sapphire Reserve, offer 3x on travel, which includes travel agencies. Therefore, you need to weigh the extra points if you have the Platinum card and don't have another card with a points bonus for travel categories. (Many cards that offer 3x on travel offer trip delay insurance, whereas the Platinum card does not)
Mistake Fares- For Mistake/Error Fares, I highly suggest booking directly with the airline if it is within $50. The airline may try to cancel the ticket, and it is much easier to work with an airline to reinstate the ticket than the airline plus a travel agency.
Priceline Best Price Guarantee
If you find a lower price and book with Priceline.com, Priceline will refund you 100% of the difference. However, it must be the same airline, flight numbers, travel dates, airports, number of ticketed passengers, cabin, and class of service. Additionally, it does not apply to fares that are not available to the general public (e.g., British Airways' AARP discount).
If you need the ability to cancel within 24-hours, you may want to consider Priceline and have them match the price on listed at a smaller travel agency on Momondo. You will have to call 1-800-774-2354 within 24 hours of booking and Priceline will have to verify the price is still available when you call. The disadvantages are that (1) it may take 10-20 minutes to call Priceline, (2) the sale price may disappear, and (3) Priceline may find some reason to deny your claim.