Thank you ropas2 - complete oversight on my part and have edited the OP. That just adds another issue...how the hell do I choose!? I want my Kronos to ring through just as beautiful as it sounds and have the ability to run my guitar utilizing the Cab sims on the Axe-FX. My only concern is overloading the speakers with too much at once.
**Update**
So after contacting support for both Atomic and Mission I wanted to add some notes here for anyone else considering the same scenario. I sent the same question to both companies: "I have an Axe-FX, but I also have a Korg Kronos that I use for my instrumental tracks. How would the *Gemini/CLR* hold up running both the Axe-FX and the Kronos at the same time? Would it have enough power to run both without overloading? I know how it reproduces the Axe-FX, but would it reproduce the amazing sound and clarity that the Kronos produces? My thought would be to purchase two and run stereo (left outs to one, right outs to the other) unless you would recommend another option."
-Atomic: I emailed support at 2:26pm. I received a reply at 2:39 from Tom King himself completely addressing each of my questions. "They would indeed be able to handle the Kronos and Axe-FX at the same time. The Kronos will sound amazing! There are even two independent inputs if you want to separate them without the need for a mixer." - This is exactly what I am looking for and huge thank you to Tom for the response and great customer service.
-Mission: I emailed support at 2:19pm and received the first response from "Mission Support" at 4:40pm. "Gemini 1 has a single analog input, a USB audio interface, and a Bluetooth wireless interface when that option is selected which can be used simultaneously via the internal mixer. There is no problem in theory running multiple signals through the Gemini at the same time, in the same way that you can run multiple signals through a PA. My question would be how are you intending to connect the Axe-Fx and Kronos to the Gemini(s) at the sane time, would you use an external mixer?" - This didn't really answer any of my questions, just kind of raised my eyebrow a bit.
I received another response at 4:43pm giving me another option that I was not considering: "One way to do this if you are not using an external mixer, would be to use a Gemini 2 and connect the Axe-Fx to one side and the Kronos to the other. Gemini 2 has two independent channels." - So this really got me questioning what the Gemini 1 was all about. Their product page and picture clearly show two XLR-1/4" combo jacks and a USB port. I replied at 5:10pm: "I'm confused. The description page shows: I/O Input 1 – Combo XLR-1/4″ TRS jack line input (mono or stereo) Input 2 – Combo XLR-1/4″ TS jack instrument input. And the pictures show Input 1 and Input 2 - Would I not be able to run 1 line form my Axe-FX and 1 line from my Kronos to the same Gemini?" I received the next response at 6:20pm "Input 2 is the analog input into the USB audio interface. It's for connecting an instrument when using Gemini with PC or Mac based software such as Protools or Logic. Mission Support" - So what this means is that while you can connect another instrument to "input 2" it will not play out of the speaker, only out to whatever your USB is connected to.
In summary: If anyone out there is looking to run two instruments into one monitor without the use of a mixer, based on the 3 products (QSC, Atomic, Mission) it seems in regards to product quality, other reviews, and customer service level alone that Atomic is the clear winner for me. The QSCs never gave me that "I love that sound" feeling, and while you have an option with Mission in the 2x12 Gemini 2. For me the 2x12 doesn't work as I only need (2) 1x12s setup in stereo(I want my pans to truly pan L/R). Sorry for the long winded comment but I hope someone finds the info useful.