I have built a number of high-performing teams and defined the respective processes.

Honestly, I don’t think you are asking the right question. Asking for the simple red or the blue pill may be tempting, but it will not get you the results you need. For Scrum or Kanban to work out of the textbook, certain assumptions need to be met (which is rarely the case).
So in order to really improve your situation, you need to

- start with your customers, and understand how you serve them. What is important? What makes their day, and how do you make an impact?
- where is your risk? Is it with developing the wrong product? Or with being too slow/too late?
- do you have stable requirements, or would you need to adjust rather quickly?
And there is more depending on how you operate, or want to operate in order to succeed.

The right process for you needs to be derived from this, and then iteratively refined.

Sorry, this is more work than you looked for, but it will save you a lot of headache trying to make a blueprint work that never fitted in the first place.

Don’t bet your company on a method - shape your processes according to your situation. Get help to get it right.