UK School VS Regionally Accredited US School

[Merlin]

Looking to continue teaching in North America. Currently instructing at a college right now with an AACSB accredited MBA.  I would like to complete my PhD online.
Debating attending a UK school (Leicester) versus a regionally accredited American school (Liberty).  

Which do you think would be a better school to attend for someone who would like to continue teaching in North America?

Well, it ultimately depends on where you end up wanting to teach. Where are you teaching now? If you want to teach at a top-tier US school (particularly at the grad-school level), you'll want to limit your search to AACSB Ph.D. programs unless you aim to move outside business. That said, finding the right online AACSB Ph.D. program may be a pain though since there aren't many to choose from, and you'll be paying out of pocket.

Honestly, if you don't care about AACSB, you'd be better off looking for a local Ph.D. program where you can get your tuition and academic costs covered. Though that will be hard to do if you're working as a teacher full-time... unless you can do it at the school you're currently teaching at. Your school may provide a means to do both.

Failing the above, it comes down to reputation. A well-regarded UK school will be superior to a less well-known US school. In this case, Leicester is better regarded than Liberty, so it's probably a stronger choice.

Aside from reputation you also need to make sure you find a school that matches your academic and research interests, and a graduate advisor that has a good reputation in the field you're pursuing. When applying, they will ask you about your research interests and what you're looking to do. They should tell you early on if they have available advisors in your research area and if they have open slots for new Ph.D. students in that area.

Be sure to set up a call with the proposed subject advisor(s) for whichever schools you're applying to. You'll be working with that person for 3-7 years so you'll need to make sure that you can get along and you have compatible goals. You also want an advisor with a good reputation in the industry, as their reputation will color yours when applying to jobs and research opportunities. A good reputation will open doors for you, while a bad one may make those doors harder to open. Most will have a neutral rep which won't really impact you in a good or bad way. If you can find an advisor that you like and has a great reputation in academic circles, that is the best. You may also want to review some of their published journals/books to familiarize yourself with their work as part of the review. This will make for a much more effective initial interview/conversation as well since you'll be able to ask well-informed questions.

Anyway, that is a long-winded way of saying, "it depends". It's not just about comparing schools, you need to assess their reputation, accreditation, and quality. The latter is often represented by their graduate advisors and research budget, etc. If you're doing remote, you'll also need to consider cost and time investment. You'll need a part-time Ph.D. if you're working more than part-time, and many schools only offer full-time Ph.D. programs.

Good luck with your search. I'm doing the same thing myself, though I'm not looking to start until 2021-2022 so I'm taking things slow.