A simplistic calculation will show it stronger with vertical supports all the way to the top. Your "end support points" for the horizontal member moves inwards. It is resting on those angle brackets, not the verticals. So you effectively reduce the span by several inches. Reducing the span reduces the deflection. However, as above, I do not trust those screws in the channel. All that force (1000 pounds / 4) is held up purely by the friction of the nut and bracket against the channel.