Johnny English Reborn is a good example of the sequel being better.
1) The main reason I love this second film is because it allows Rowan Atkinson to show Johnny English developing into a better MAN. The first he was sort of like Mr. Bean gets his chance to be a spy...which was great and enjoyable but wore on towards the end. Now you get to see him not only as a veteran agent who STILL has to adapt to be BETTER. I like this character more. He seems more real and relatable to me. Maybe I see myself in him more. His having to deal with women bosses/technicians, having to teach a new partner, and his agency becoming more political and less of just the old boys club of the past allows the film to become more film of the 21st century instead of just a spoof of the 60's spy genre.
2) The co-stars/side-characters were better. The love interest was more interesting and had a better face/body. She seemed more believable also. The new female Pegasus was great. The top agent was good in how his upper-crusty manner was used as a good contrast to English... and how Engilsh reveres his senior for his aristocraticness and how that comes to bit him in the end is great. I like the new young enthusiastic partner. I like the way English reminds him when he quits that UK is also HIS (the partner's) country to defend also.
3) The action, vehicles (car and helicopter), technology, and fights are better. Most important...they combine all this "spy film" type stuff WITH the comedy without taking away from one or the other.
4) The comedy itself was well thought-out and had me laughing more often. For example the scene where his boss gets mad at him and he has to respond to her after taking the voice changing lozenge still makes me crack up. I mean it is like two jokes in one. AT first you are thinking his voice went high because she verbally castrated him in front of the tech boys...which is silly enough but then you realize he had accidentally taken that silly piece of spy-tech that really works..but was not quite ready yet.