First, Sony's Official Power Cover, the CP12: (http://www.amazon.com/Sony-CP12-3000...dp/B00FX2MG3Y/)
Battery Size: 3000mAh
High quality feeling case.
Uses with/supplies the magnetic charging port
Has a slot for/supplies a stylus.
By far the most expensive. The other two options aren't even in the same price range.
Makes the Z Ultra bulkier than before; By others accounts it's about as big as a Nexus 7 now.
The stylus isn't tightly held and will slip out with little fuss.
Conclusion: While it's high price is very off putting (I picked it up during the winter sale when it's price was a bit more managable), as a case it's very high quality. Dispite slipping in and out with relative ease, I find it usually doesn't come out unless I want it to. I find for casual to medium use the battery supplies an adequate backup charge. In terms of in the hand feeling it outclasses the other two options without even putting up much of a fight. That being said, at it's high price point, it may not be entirely worth it.
Overall, if you want to use something officially made by Sony with a high build quality that can provide an adequate charge if need be, this is what to go for. Still, price for price, it may not be worth it.
"Brando Power Case" (http://www.amazon.com/Aftermarket-Pr...dp/B00G9RCSHG/)
Battery Size: 4500mAh
Thinnest case with the most minimum bulk added.
Feels decent in hand
Charges with the proprietary magnetic port, but takes a Standard Micro USB for input.
Cover feels flimsy
Questionable build quality
Conclusion: OK, so first, I put the name in quotations because for the life of me it's hard to find what on earth this case is actually called; The one I bought came straight from a shop called Brando; Google it if you desire. However, the one I received flat out didn't work. My phone neither recognizes being plugged in nor does the case act like it's charging something. Which is unfortunate, because I actually like the overall feel of this case. If it were to work (And if I weren't just one of several cases where this case is reported as faulty, I'd write off my experience as a one off), I'd say it outclasses the Sony case without question. The lack of stylus support isn't, in my opinion, worth mentioning; If you need a stylus, just carry a pencil with you.
Overall, if you're willing to risk getting a dud product, go ahead and go for this one. If it works, you'll get a nice feeling case with a much better charge than the CP12
"KingsMansion Battery Case" (http://www.amazon.com/5000mAh-Portab...dp/B00FWP8FKU/)
Battery Size: 5000mAh
Biggest battery of the lot
It's textured back grants protection against slipping.
Has the best grip on the device of any case here.
Textured Back feels weirder in the hand.
Even when plugged in, it will only charge the phone when the switch is on.
Conclusion: I haven't had much time to deal with this thing yet, since it just came in today, however, I like what I have for the most part. While it's the hardest of the lot to put the Z Ultra into, it also has the best grip on it. It will NOT come out without you meaning to take it out, but it's also fairly easy to remove when you do. It provides the best charge to the Z Ultra, clocking in at 5/3 as strong as the CP12, and being as thin width wise as the Brando one. However, the textured back feels different in the hand compared to the smoothness provided by both of the other ones. I don't get the same feeling of questionable build quality from it as I do from the Brando case, however. Oh, and like the Brando case, I have no clue what to actually name this case; I got the name "King's Mansion" from the seller on the Amazon page, but the actual box doesn't have any company name on it as far as I can see. As a side note, it's a thick case... I'd say just eyeballing it that the back of the case is as thick as the Z ultra itself. I personally think this is fine since I think the Z ultra's a tad too thin anyway, but it's up to you.
Overall: Cheapest, best grip, thinner than the CP12, and has the biggest battery. While it feels a little worse than the other two, it'd definitely worth the price. I'd pick it up on Ebay over Amazon (I did), just because the amazon one has aweful delivery times to the US, but choose as you wish.