Auto body repair & detailing: Bumper replacement Vs Repair, bmw 525i, rear bumper

Question
Hi, my car (05 BMW 525i) was rear-ended on the bumper and there's screw marks and scratches on the bumper.  I went through 3 body shops, and 2 recommend it to repaint and 1 just estimated it to replace a new one at a higher price.  The other party's insurance company has agreed to pay the cost, but I'm wondering what should I go with?  Should I replace it or just repaint?  Replace sounds better for me, but I would like to know if there's any difference in the two options.  Any pros and cons.
Also, the replacement body shop make an estimate on the "Rear Bumper Cover" part for replacement, but I see the damage on two parts, the bumper and the skirt on the vehicle.  I'm wondering if it is two parts for the vehicle of that model, or it just refer to as rear bumper cover.  I'm afraid the body shop will only repair the one part, and leave the other.

Answer
If the lower textured piece is part of the bumper cover then the whole bumper needs to be replaced. If the lower part is a separate piece then I would recommend repairing the bumper cover to save your original VIN sticker on the part. This sticker will not be on a new part and is a tell tale sign that the vehicle has been repaired thus lower resale value.