BA awards will have fuel surcharges like any other program. I dont think they charge fuel surcharges for other awards. AA for 40k off peak in coach r/t is a good value.

One note though. Alaska's award chart is US-based which makes sense since most of its members are US-based. If your award travel is only US-EU its fine but if you want to do anywhere else you might have to do two awards and connect in the US. I would personally credit DL/AF/KL to Alaska and credit BA flights to its own program. Its distance based and very valuable for short flights within Europe.