Ok, I am now at a keyboard and not on my phone, so here is a bit about it. A long handle creates a larger radius about which the angular velocity is active, so for a given angular velocity, the linear velocity at a point below the pivot is going o be slightly higher due to the inch extra length.
What you also have to take into account is the moment of inertia (MOI) of the bat. This affects the ability to swing the bat at the angular velocity. The greater the MOI, the slower you will be able to swing the bat. Two bats, one long handled and one short handled with the same profile will have different MOI. The LH will have a greater MOI than the SH as the MOI is dependent on mass and distribution of mass over distance. This means that the angular velocity of a LH with the same profile as the SH is going to be slightly lower. The result is that the linear velocity at the point of impact is going to be slightly different.
To achieve the optimum performance, there is a delicate balance. As I said, it's not as straight forward as simply length of bat handle! The basic concept is that it is not the total overall weight of the bat or the length of the handle which determines how fast you can swing a bat, but the way that weight is distributed along the length of the bat.