We don't know what you think a "half-Wilson" mirror is. If you want to compare two circuits, show the schematics of both of them. Also the current would be a step, not "ramping" up and down. Do you mean the voltage ramps up and down to nearly both rails?

@Olin, sorry for not being more clear. Edited to hopefully clarify what I'm asking. I didn't mean that it is an intentionally controlled ramp, rather that the output (i.e. collector current sunk from the node at the top of the cap) takes measurable time to go from 0 to the value that it will have. I sort-of think the 3rd transistor would bring in extra current from the output side, but maybe this is offset by having another transistor to turn on, hence thought I would post the question.

Use a simulator. Really, use a simulator. If you are not able to use a simulator let me give you some very, very good and strong advice: Get a simulator and learn how to use it.

@Andy aka -- yes, you are right. It's something I have been avoiding. Thanks for the push to get me there.