I've been breeding, raising, training, and FEEDING, coon hounds, rabbit hounds (my main passion) and Hog hounds for the better part of 40 years now. As I told you in another post, I cut my hog hounds out because I just don't run hogs with dogs like I used to (age does that) so keeping the poor things in a kennel all the time without hogs around here to keep them in fit shape was detrimental to my dogs so they went to a good buddy down in Texas where they will get dang near DAILY exercise!!
The "mix" you are proposing would more than likely end up in a fairly good herding dog with a pretty much useless nose. It would also probably end up WAY too energetic to be a house dog as well. Cat's and Brit's both are extremely energetic dogs. The pups would more than likely have very sharp eyes and would "sight hunt" like a demon on steroids with the likely foot speed they would have. It would be a tossup as to what kind of mouth they would have for baying. If you can't hear your dogs on a hot trail they are pretty much useless to you. Hearing a good bay is much faster than trying to track them with a GPS. Brits aren't a bay hound and have "soft" mouths. Cat's don't have the best mouths either but they are 10 times better than any upland game bird dog.
Granted everything I wrote in that last paragraph is merely "suspicion" but knowing both the breeds fairly well I would have to bet on my "suspicions" to be pretty much correct. The breeds that you are trying to "mix up" are just too far apart in their "job skills" to produce a viable working dog for hunting. Then again, you may end up with a littler of Cat's or a littler of Brits depending on which dog has the most dominant genes. When trying to come up with a good mix to create a new breed for a specific "job" you don't start from the furthest away specifics but the closest and work the breeding outwards till you end up with the desired effect. It takes several generations to create a specific dog unless your "job requirement" is similar to both dogs. Like breeding a Pit with a Cat. You would more than likely have either a dog with a great nose and a powerful body OR a dog with an "ok" nose and iron clad jaws with fantastic foot speed.