I've bagged plenty of bunnies and birdies with a scoped drilling and scoped combination. I've even successfully shot trap with them. The trick to it is to have a low-magnification scope, mounted so that you can easily look through it without moving your head. A lot of Euro drillings and combos come with scopes which meet neither criterion, but it can be fixed. For a bolting bunny or flushing birdie, with your correctly-mounted low magnification scope you simply focus on the target - looking through the scope but ignoring it - swing and bang!
If you see something sitting a bit further away, it is easy enough to wind on a bit more magnification if you need to do so.
