While that seem like it would make sense, it has not been my experience. A high quality break barrel is every bit as accurate as an underlever of the same quality. High power super fast models of either type are hard to shoot. Find something like an R7 or R9 from Beeman and they are easy to shoot well. The 460 that I had was not difficult to shoot either but it was not the Magnum version. It did have some issues when cocking where the lever had to be perfectly aligned with the barrel or it would bind and grind (actually found some metal shavings in the action). I have had limited experience with a Model 48. While it shot decent that was a huge, heavy, beast of a rifle and did not appeal to me at all. Every time I went to load it, it felt like messing with a loaded bear trap - if that cocking mechanism ever slipped while loading - bye bye finger. Best advice is to forget high speed ratings, find something that is medium powered, high quality (German made) and you will have a smooth shooting rifle that will last a lifetime (at least). There is 'no replacement for displacement' fits air rifles also. If pest control is the main factor then .22 cal is the way to go. With .177 pass throughs are more prevalent and they just don't kill as fast. These are low powered rigs (12-15 ft/lbs) and don't kill with shock like centerfires.
A little summary of each type:
https://www.pyramydair.com/blog/2007/12/breakbarrels-sidelevers-and-underlevers-advantages-and-disadvantages/#:~:text=Sidelevers%20have%20a%20separate%20cocking,re%20less%20sensitive%20to%20handling.
