Ring penetrators are likely to penetrate more; they would be best used in an armor piercing capacity, because they have a higher sectional density for the same mass.
If you want wound ballistics, you want the bullet to deform as rapidly as possible once it hits the target, because that ensures the quickest and most complete transfer of energy from the projectile to the target, ensuring the most damage. A solid(ish) slug is better at energy transfer because it has more surface area to deliver energy, and it can deform better by mushrooming, causing even better energy transfer and enlarging the wound cavity.
As far as getting higher muzzle velocities with a lighter slug, it’s not a bad tradeoff – rounds have been moving that way for a while since k=mv^2/2. It’s easier to get more energy by increasing muzzle velocity than by increasing mass. However, for a given energy, recoil is the same, but pressures in the barrel and chamber can be higher. There’s also a velocity limit achievable by the propellant, though it’s probably not going to be a factor in a personal weapon.
The reason no one uses ring penetrators is because for small things, like rifles and pistols, they don’t perform better in wound ballistics, and don’t have any advantages as far as accuracy, etc, and have drawbacks like increased complexity.
For high energy armor piercing applications like tank rounds, they might have advantages, but IIRC they are harder to fin stabilize and can’t really take advantage of adiabatic shear (self-sharpening like tungsten and DU) – a KE round penetrates by sort of melting/eroding through armor, which isn’t quite the same as punching through meat or kevlar.
Really, the thing is that ring penetrators don’t solve any problems, so no one has developed them very far.
ETA: and I don’t recommend googling ring penetrator.