A 30.06 or .308 FMJ bullet, traveling point forward, that passes through an arm or leg, or perhaps a short wound track tangentially through the torso (peripheral hit), and does not hit bone will produce a wound no more severe than a .32 ACP FMJ.
Likewise, a 6.5mm Carcano bullet FMJ-RN bullet, traveling point forward, if it doesn't hit bone, can easily pass completely through a human torso and produce a wound no greater than a .32 ACP bullet. In soft tissues the 6.5 bullet easily travels 20 or more inches before it begins to yaw.
In 1937, Elmer Keith wrote an article, published in the July 1937 issue of American Rifleman, "Bronze Bullets in .220 Swift," in which he reports shooting several animals with 55-grain, non-deforming, non-fragmenting solid bronze bullets propelled at 4300 fps. He remarked that several of the animals solidly shot in the body showed no signs of being hit.
Therefore velocity alone is not an indicator of a bullet's wounding ability.
As described by Urey Patrick, in his paper "Handgun Wounding Factors and Effectiveness," the four components of ballistic injury are:
1) Penetration. The tissue through which the projectile passes, and which it disrupts of destroys.
2) Permanent cavity. The volume of space once occupied by tissue that has been destroyed by the passage of the projectile. This is a function of penetration and the frontal area of the projectile. Quite simply, it is the hole left by the passage of the bullet.
3) Temporary cavity. The expansion of the permanent cavity by stretching due to the transfer of kinetic energy during the projectile's passage.
4) Fragmentation. Projectile pieces or secondary fragments of bone which are impelled outward from the permanent cavity and may severe muscle tissues, blood vessels, etc., apart from the permanent cavity. Fragmentation is not necessarily present in every projectile wound. It may, or may not, occur and can be considered a secondary effect.
In the situations described in my first three paragraphs, the only components present are penetration and permanent cavity. The bullets exited the target before they began to yaw. When a bullet yaws it increases its frontal surface area, which increases the amount of tissues it comes into direct contact with, and which, in turn, increases penetration resistance and the amount of energy transfer. Therefore a bullet that yaws produces a larger diameter temporary cavity, which, depending on the specific tissues involved, may substantially increase wound trauma.
Whereas a bullet that expands and shed fragments or disintegrates as it yaws has the potential to increase wound trauma. Combined with a large temporary cavity, fragmentation can produce severe tissue damage.
In the three situations I describe above, a 9mm or .45 ACP FMJ bullet will indeed damage or destroy more tissues than a 30.06, .308, 6.5 Carcano and .220 Swift. Will the wounds be more likely to kill? Lethality is a function of what tissues are damaged or destroyed and the amount of damage inflicted. A .50 BMG FMJ bullet that passes completely through the body without yawing or striking bone will produce a wound equivalent to a .45 ACP FMJ bullet. Which one is "more likely to kill" will depend on the path through the body and the tissues the bullet comes into direct contact with.