Dani made an excellent remark, the Turkish aircraft stalled while BA038 recovered while in both cases manual override was initiated in similar conditions. According to the report following AP override the 737 attitude went 8 degrees below horizon before increasing to 22 above horizon. This probably results from the combination of a full nose up trim with application of max thrust which momentum couldn't be stopped by pitch inputs (similar as for the Perpignan A320 accident).
The remark about the low speed protections is very relevant as the 777 and the737 were certainly not trimmed the same way when crews took manual control. While the 777 could be recovered after stick shaker activation, the 737 entered pitch oscillations and stalled as full power was set.
Do you seriously think that swapping crews between these 2 aircrafts would have changed the outcome once stick shaker was reached??