3 answers
Break-action rifles are worth it today mainly if you have specific situations - tight hunting grounds, quick offhand shots, or if you already have a decent break-action lying around and don't want to drop hundreds of euros on something new. The practical tip I don't hear often: a lot of people underestimate how much a solid break-action rifle with modern optics (a decent LED red dot or compact scope) boosts your hit rate - that makes it a lot more relevant, even though the classic iron sights are slow. If you're torn between a break-action and a repeater: try out a good used break-action with modern accessories when you get the chance, that can make the difference between whether the rifle is practical for your terrain or not.
What are you hunting and in what terrain? Drilling rifles have pretty much niche status these days, but they're not completely obsolete - if you're spending a lot of time in dense brush or hunting from elevated stands where you need to switch between different distances quickly, the combination of two barrels can be practical. That said, modern combination guns or just two separate weapons are often more flexible and cheaper. For collectibles or traditional hunting it might still be worth the effort, but for efficient hunting I'd go with other options these days.
Have you actually shot with a break-action rifle before, or are you asking more out of theoretical interest?
I think you shouldn't see it in such black-and-white terms like some of the other answers do. Sure, break-action rifles aren't the standard tool they used to be - but I wouldn't say they're completely obsolete either. It really depends on how you hunt. In my particular hunting ground, they're still pretty practical because you can react quickly and handling in thick brush is just handier than with some other systems. And honestly: these things are less prone to issues if things get rough - less to adjust, less that can go wrong.
But realistically, the target market has gotten smaller. If you have a large, open hunting ground and hunt at longer distances, a modern repeater is probably the better choice - better hit rates, more flexible ammunition options, just better thought out for modern demands. For me, the real question would be: does the break-action fit your actual hunting situations? If yes, why not. If you only have it because your grandfather had one and you're uncertain - then I'd put the money into something else.
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