When using an anti grazing device for beginners, do you prefer one that attaches to just the headstall of the bridle or the ones that attaches to the headstall and down to the bit?

The only thing I don't like about the ones that attach to the bit is that they do catch them in the mouth.They are however more effective in the long run, as horses will be less likely to try to pull their heads away when not wearing one.
If you are just planning on using one at home, then a cheap fix is bailers twine tied to the bit and D-rings of the saddle. You can also make your own anti-grazing device which works great where you attach dog clips to the ends of some thin paracord/rope and use it the same way as the bailers twine.