I absolutely loved Seasons 1 + 2, wasn't sure how I'd feel about a new cast for Season 3.
The new cast is mostly excellent although I'm not a fan of Helena Bonham Carter as Princess Margaret. She seems miscast to me, her acting is very much Helena Bonham Carter pretending to be Princess Margaret. She didn't nail the character at all.
Olivia Colman is not short and petite like Queen Elizabeth which took some getting used to after Claire Foy's portrayal but she won me over after a couple episodes. She is a very talented actress despite the criticisms I've seen. Claire Foy was a hard act to follow but I believe she's done it. Tobias Menzies is amazingly spot on as Prince Philip in mannerisms and personality.
The story line can be a bit slow at times as many of the episodes revolve around political and world events and less about their personal lives. It is fitting though, considering that the 1960's were a time of major social change in many aspects vs. the 1940's and 50's when the first two seasons take place.
Overall I enjoy the show as much as the first couple seasons and will continue to watch.