Is it safe (for the backhoe, not the operator

) to pull logs out of the woods with the backhoe bucket? Or is it better to hook the logging chain to the FEL, and drive in reverse? I am thinking about the stresses on various parts.
Neither is a good Idea.
Reverse you will have less power and limited mobility.
And you do NOT want to chain to the bucket and pull with the tractor. The ONLY way you should pull ANYTHING at ALL if attached to the BH is with the BH's own power, NOT the tractors.
The reason for this is simple, as you are pulling, the force of the log will try to extend the hoe out, thus trying to collapse the dipperstick cylinder. There is NO PRV between the valve and the cylinder. So the ONLY thing that will limit the pressure that builds in that line is the amount of pulling force supplied by the tractor.
And rest assured, the tractor has WAY more pulling power that the BH. You will blow the line off if you attach to a tough log. What he do you have? is it the 753, 754, or 755. Because dads is a 755, which has 4.5" cylinders. And it only has a crowd (dipperstick) force of ~5000lbs at the rated 2200psi capacity. So in otherwoods, of your pulling force exceeds that, you are incucing more pressure in that cylinder and hose that the BH itself can provide.
You'd be really suprised at how much you can indeed pull, even with R4's. These machines are in the 11000lb range. It will outpull a farmall H (as mentioned earler) any day of the week.
If you have decient R-4's, given the weight of the machine, it will probabally pull double that. And thus, you are putting 4400psi in that cylinder and line with NO PRV. See the problem???
So basically what you need to do is come up with a good and safe hitch point that does NOT impart any forces on hydraulic cylinders. Perhaps through those two holes under the operator platform of the hoe?? That is what we use on dads 4500 to pull with as well as tie it down to the trailer.