Break Opens are more flexible...pun intended

For general hunting, the accuracy with most handguns (Generally speaking) is beyond or as good as most hunters need.
Want is a whole different matter.
XP's are typically more accurate, or at least can be for a variety of reasons: Stronger action, you can free float the barrel, faster locktime, better balance (With center-grips), better triggers.
For varminting or sustained shooting you do not have to disturb the whole handgun off of your rest to relaod like you do with a break open.

Break-opens will be less expensive. Break-opens like the TC's have interchangeable barrels. You can do switch barrels on bolt rigs, but it is not as easy. TC's can be more compact and lighter weight than a XP.

Each has their strengths and weaknesses.
Nothing wrong whether you prefer one type over the other, like both or dislike both.
You will not see break-open actions (Rifle or handgun) in high accuracy games, whether short range BR (100, 200, and 300 yards), 600/1000 yard BR, F-Class, Tactical matches, etc...
It would not be fair to expect them to perform at that level...they were not designed for that.
A bolt rig will not be as finicky as a break open is, especially in terms of pressure and sticky extraction.