I always prefered the Poleaxe to the elegant version, but that is just me.
Personally, I would use the weapon that covers your largest frustration. If shielders give you a very hard time then the poleaxe will be a better choice as it has a high damage which allows it to exploit the "bonus against shields" rather well. It also has appreaciable better reach then the Bec. However, the bec will perform better against armoured targets, so if you feel you are not taking them down fast enough then I would choose the Bec. As for the popularity thing, they are both about equally common in my opinion (roughly) so don't worry about that.
If I had no alternatives and had to choose between the two, then I would personally go for the Poleaxe as I don't like fighting shielders, and your 8 PS will allow you to take targets down fast anyways (the extra length of the axe will allow you to hit horses a wee bit easier too).