Intra-oral is a more painful recovery because swallowing and eating etc is worse, with external surgery you can still sometimes have trouble opening your mouth wide but it’s generally not as painful.
There is better visibility for the surgeon to see the nerves, and the facial nerve should be monitored during surgery, so this is usually regarded as safer…ES can cause the nerves you mention to be compressed or irritated, so hopefully removing a decent amount of the styloid process will help with the nerve pain you have.
As for scar tissue, this could form whichever way you have surgery as muscles would need to be cut through to access the styloid, so I wouldn’t think this would make a difference?
Icing the neck around the incision with an ice pack (not directly over the incision) will help with swelling, and sleeping propped up helps too, whichever method you opt for. So no difference in what you’d need to have ready…
There’s info in the surgery section on the site if you have time to read it:
ES Information- Treatment: Surgery - Welcome / Newbies Guide to Eagle Syndrome - Living with Eagle
Had a quick look for research papers, there are more links I’m sure…
Transoral Route or Transcervical Route? - General / Research Papers - Living with Eagle
Best wishes for you surgery, thinking of you & praying for good results 
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