Anyone of the 2 would work for your application. I see nothing in your parts, and nothing in your stated goal that lead me to think one is better over the other. Myself, I stuck with Yocto.
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Ubilinux is Debian-based so if you’re familiar with any Debian distribution Ubilinux would be a good option. But, as Romonaga said, in terms of functionality both distributions are capable of handling your project. The only difference I can think of is regarding the support that you’ll get. For the Yocto image, you can post any question that you might have in this Community. For Ubilinux, the EmutexLabs guys are the ones in charge of the support.
If you’re going with Yocto, this is an excellent thread https://communities.intel.com/thread/101059.