And since CEO effectively can work in a Cookie based build and in fact helps fuel the Cookie-Cream combo, I think I'm just going to skip ahead to comparing Cookie and Amatecrossu.
First, a rather obvious one. Base power, and as the meta moves forward into a more and more aggressive state, the importance of these numbers become more and more evident. Cookie sits on the rather average 10K power, putting it up to risk against 12K attackers and the surplus of Vanguard+Booster combos that push around 10K Vanguards. Compared to Amatecrossu, who sits on 11K base, and 13K as a Cross-Ride, the numbers play far against Cookie in this category. Of course, I can't really place any straightforward numbers to compare these two base powers, but it certainly is an area Amaterasu reigns far superior.
And while base power is fine and dandy, another factor including power levels comes into play. Between the 2, Cookie is the harder hitter...sometimes. For the sake of a fair comparison, I will assume both are being boosted by Milk. Since both units are hitting 20+ through the midgame in this case and since neither would be guarded/have a real effect on the midgame through attacking, I'll be focusing mostly on the late game. Now, counting Cookie's Limit Break, Cookie will be striking 25K, while Amatecrossu will cap at 23K. Essentially, Cookie will almost always strike the ever common 10K Vanguard harder than Amatecrossu, and will sometimes surpass Amatecrossu at hitting Cross-Rides and MLB. This is great and all, but maybe hitting 1 stage harder depending on your match up vs having superior defense regardless of match up, well, I'd much rather Amatecrossu for this. If only Cookie could make good Rear-Guard columns, with cards like...
Battle Sister Cream. Cookie's personal booster and a pretty interesting choice for a 21K Rearguard column fueled by CEO Amaterasu. Aside from that however, this pushes Cookie to always outperform Amatecrossu while facing 10 and 11Ks, Vanguard or Rearguard. This just about makes up for the defensive measures Cookie lacks. To those keeping score, that basically means we've come to an even match up.
And yeah, I did just break off the whole 'fair comparison' thing with Cookie.
And now for the tie-breaker. Amaterasu's Limit Break seems more than effective on paper, but put it in practice, we eventually come crashing to a halt. To break it down, upon Limit Break, you may search up to one card in your deck and add it to your hand when you hit. Backtracking for a moment, Limit Break. This skill is one that only works in the late game, yet clearly is a skill designed for mid-game usage that fails in the late. Why this happened is beyond me and honestly it's really hard to justify as the many situations that it is properly usable either means your were losing, or that you are winning anyways. Cookie on the otherhand, works better for the 2 Counter-Blasts you have to spend. While not nearly the quality you get out of Amatecrossu, Cookie does an amazing job at cycling your hand and overall keeping your own card advantage in check, allowing for better hands and advantage in general. Reriding, her skill also counters the ride's -1, basically meaning you cycle out a Grade 3 and another card of your choice for 2 newer cards. Maybe it's because I just can't justify Amatecrossu's skill, but overall, this is Cookie's victory here.
Overall, while Amaterasu's Cross-Ride status is a powerful asset, Cookie is a far more flexible card better suited overall. Between the versatile beater who can cycle your hand or the virtually vanilla Cross-Ride, I declare Battle Sister, Cookie the winner. Post below your views, any arguments I may have missed, and your own verdicts of this match up.