I've always preferred Here's Lucy over The Lucy Show because her real kids were on it rather than the fake kids of The Lucy Show. Also, on Here's Lucy, it made more sense that Gale Gordon played her brother-in-law and boss, rather than just a boss like in The Lucy Show. Since they were family in Here's Lucy, it was understandable that he'd put up with her mistakes. Whereas on The Lucy Show, it never made sense that Mr. Mooney would keep her on when she was such a mess.
I was also disappointed that Desi Jr wasn't used as much as he should have been. He was talented, good looking, and could have been a real asset, but instead they chose to showcase Lucy's comedy, a woman who should have learned by then to act more mature instead of acting endlessly goofy. After all, we do learn how to behave like adults at some point (usually). I was extremely saddened when Desi Jr decided not to continue because I preferred the family format of Here's Lucy: Lucy, Kim, Craig, and Harry.
The best part of The Lucy Show for me were the episodes with Vivian Vance and Mary Wickes.