Heh, I did the work a while ago, but never bothered posting or saving it. So gonna do it again. ;)
Assume the Junction Minion is of the same minion count and size as the UC minion. Assume tattoo's are being used at MTL (33% of minion size).
Both get to use HoE, and EB. so these can be ignored. The Minion will get the Benefit of an AoF (+10) and Either a Gi+EC (+13) or ToA. HG will be ignored for the minion, but double dips for the Jig, so in the end the Jig will get +23 to UC (from a +15 HG).
HP: 0.5 * 0.33 = 0.165 = 16.5%
ST: 0.25 * 0.33 = 0.0825 = 8.25%
DX: 0.5 * 0.33 = 0.165 = 16.5%
UC: (0.5 * 0.33) + 1 = 1.165 = 116.5%
Minion with Gi + EC
The minion will try to match the Intrinsics of the Jig
DX: 14.6 * 1.13 = 16.5%
UC: 60.65 * 1.13 * 1.3 = 89%
Close, but no cigar. The Jig also has +13 UC levels over the Minion, after XP has been spent.
Minion with ToA
ST: 0.5 * 0.33 = 0.165 = 16.5%
DX: 0.33 * 0.33 = 0.1089 = 10.89%
UC: 83.5 * 1.3 = 108.55%
So quite similar. But
I think originally, I left out the double dipping of the HG for the Jig. :(
Even with a ToA, while the stat distribution is similar (ST and DX swap places), and the extra PTH the ToA gives (which doesn't stack well with UC), the Jig *still* has +23 UC levels over the minion after all is said and done.
Looking at this now, I don't think there's any way a UC minion can compete with a Junctioned Familiar.
And that's sad. :(