Any hunting rifle round will do this as well, except the smallest calibers like .22 LR that are meant for hunting squirrels and the like.

But also, no, the smaller rounds don't have a "tendency to bounce around in the body". It sounds like you're referring to the phenomenon known as tumbling, where the wound track ends up being curved because the bullet loses stability as it hits. This happens because bullets are heavier at the base and thus unstable; while in air, they are stabilized by rotation imparted on them by the rifling, but once they hit anything dense (like, well, human body) it would take a lot more spinning to keep them stable, so all bullets do that. It does not involve any bouncing, however.

Light and fast bullets like 5.56 are particularly unstable and will do it faster, though. But even then, for 5.56, the primary damage mechanism is from bullet fragmentation: between the bullet being fairly long and thin, and high velocity of impact, the bullet literally gets torn apart, but the resulting pieces still retain most of kinetic energy. Except now, each piece, being irregular, travels on its own random trajectory, creating numerous small wound channels in strong proximity, which then collapse into one large wound cavity. But, again, this is mostly a function of bullet velocity and construction (e.g. presence or absence of cannelure), not caliber as such.