Emitter current and Early effect
following up on comment of "LvW", the mechanism would predict the highest_Beta transistors will have the least Early Effect (have the flattest I_out).

And because there is a small region of bulk silicon between the base contact for metal and the actual base region that is sandwiched between emitter and collector, with the Ibase * R_bulk_base == voltage varying as Ibase varies, it sees the LOWER NOISE transistors (which have lower R_bulk_base) will have lower Early Effect.

I realize the parameters we use are Abstractions, are parts of modeling.

SUMMARY: I'm thinking high_beta low_noise transistors will be the best current sources.