Use Amex MR points to book flights via Amex Travel or transfer them to a frequent flyer program?

Flights & Airfares
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1

I am a member of Amex Ascent program and am looking at booking an overseas trip with family.
Generally speaking, will my points be more valuable booking the flights through American Express Travel or transferring them to a frequent flyer program and then booking?

2
If economy then I think Amex travel would work out better. You would also earn points/status on the fight from the airline
If higher classes then better to convert to airline program first
3