Most of the info can be carried over from my review on the first 201 episodes found [Here]. There is no real transition or distinction between the 2 seasons for Gintama. It changes nothing in its formula except some modern updates which is exactly how it should be.
The major differences over the first 201 episodes are as follows:
-Widescreen aspect ratio change, finally!
-Improved art and sound quality
-Improved comedy. These episodes feel quite a bit more funny than the first 201 (Episode 237 & 238 are pure gold)
The only thing striking me as missing in these 51 episodes is Sadaharu </3
A flaw at fault from the subbers and not the show itself, the extra information and referencing seen at the top in yellow is no longer there which is unfortunate. It makes it more difficult to pick up parody or educational information when it specifically references to something.
Any extra information though, would be redundant. See link if needed for further details.