How to redesign without losing yourself

We’ve been doing a lot of redesigns this year.  Some we do ourselves and some designs are supplied by agencies.  Everyone thinks their new design is better.  And it’s true visually they usually are.  But are they better functionally?  Is it a new coat of paint or did you knock down some walls?  Will your customers even recognize the new you? How about search engines?  Will this fab new look kill your SEO?
Here is an interesting inforgraphic from Neil Patel from QuickSpout that’s good reading.