It's a great question, and Avios is quite confusing. So, let's start with a few things that you want to keep in mind when transferring from AMEX MR (Membership Rewards to Avios).
#1, You will want to try to transfer when there is a bonus transfer period. This can be a 25% to 40% bonus for transferring from AMEX MR to Avios. This tends to happen once per year for about a 60 day period (I could look up the historical data). IIRC, it occurred last year starting at some time in August.
#2, Avios are great for some uses, and not so great for other uses:
Excellent Uses
-AA Award Tickets in the USA and to Hawaii (so domestic award tickets on AA)
-Intra-Europe Award Tickets (both in economy and Club Europe - also remember, when you redeem Club Europe even for a short flight within Europe you still get benefits like lounge access)
-Intra-Asia Awards
-Upgrades (especially from revenue WTP-World Traveler Plus, premium economy to Club-Business Class)
#3, Using Avios for transatlantic will mean you have to pay very high YQ (taxes and fees) for premium cabins. This often makes the redemption far less valuable.
Some background:
My award travel journey... (this is a great example of effectively using AMEX MR points) which is very constant since 2/3 kids live in the USA and most of my relatives are in the USA. Our #1 go-to from the East Coast (JFK and BOS) have been DeltaOne award tickets ex-USA using FlyingBlue miles. (Low taxes/fees, low mileage and decent availability... also booked one west coast trip back to LHR last year...) Ex-UK/EU is trickier. For myself (and those in the fam living in London), I buy during luxury sales and also will consider positioning ex-AMS instead of flying nonstop ex-LHR if it's a good enough deal. (I also value my OneWorld Emerald status and need to qualify each year...) Of recent, I have been trending around £1300'ish ex-LHR to the USA roundtrip in Club (biz) with upgrading to F about 40% of the time. I'll sometimes "jump" on a £800'ish ex-AMS USA roundtrip fare if I can work it out since I lived in AMS for 3 years prior to London and it's always fun to visit friends.
Most Recent Example (all possible using AMEX MR Points transferred)
Recent award travel booking for my father and stepmother (they live in Northern New Jersey):
DL JFK-LHR (DeltaOne) 86,500 miles (for two, due to AMEX bonus on transfer to Flying Blue) + $30 in taxes
BA LCY-JFK (BA1 Club) 100,000 miles (for two, Avios) + $1120 in taxes. (We also do transfer AMEX to Avios when there is a bonus, but I tend to bank and earn a decent amount of Avios)
(This is BA 1, which is the A318 with 32 flat bed seats in a 2-2 arrangement - my parents thought it would be fun to try. Their last trip, we did BA First LHR-JFK with First Wing and CCR.)
So, what do we have here:
186,500 miles (2 people) + a total of $1150 for two people to fly on the exact flights they wanted nonstop to/from London. Obviously, a little “sharpness” on the ex-JFK.
Or, 92,250 + $575 (roundtrip per person).
But, the end of the day. It was much easier getting BA flights (award tickets) back to JFK or EWR than DL with Flying Blue from JFK to LHR (still not that bad). Options for LON-NYC were like 12 flights over 3 days +/- including also EWR and First or Business Class. Taxes (YQ) are the same for BA First and BA Club (or BA1). Bonus: My dad LOVES the VS arrivals lounge at T3, and I love it when my folks are happy. (Delta uses the Virgin Arrivals Lounge at T3 and the Virgin Clubhouse for departures from LHR T3.) I fear that some FlyingBlue devaluations are on the way.... so, the party might be ending soon. We shall see.
Conclusion: You sort of have to determine where you want to go, and how to most effectively transfer the points.
I would be happy to start a series of articles on LVA Travel, about transferring MR points and redeeming Avios and also FlyingBlue. I could start from the beginning and walk people through the steps and best options. We could follow-up here (in the forums) for sure, with questions.
This all might be a "bit much" to absorb, so please do ask questions, I am happy to explain further.