If you want full resolution 4:3 then shoot 4:3 and letterbox for your other version.
The loss of cropping off the sides if you shoot 16:9 is negligible so really you could go either way.
I guess one advantage of shooting 16:9 is that you future proof the material for use later on.
(if that’s of any concern)
If you do decide to shoot 16:9 make sure the camera shoots native 16:9 and not a digital conversion
like the XL1, DVX-100 or the PD-150/170.