The DVD versions are four 90-minute long movies. The TV/Hulu versions are sixteen 22-minute long episodes, which are edited differently, with some jokes cut, some added, and new opening credits “tagline” jokes that aren’t in the DVD versions (since they have one opening credit sequence for each film, rather than four for each when they were edited into episodes for syndication).
I haven’t seen all of the episodic versions, so I don’t know what all is different in detail.
You can find the differences listed on Infosphere, the Futurama Wiki.
For example, here are the film to episode edits for Bender’s Big Score, Part 1:
https://theinfosphere.org/Bender's_Big_Score_Part_1
The introduction is moved to the beginning and instead of the whole cast, only Zoidberg is still seen in a character shot. The Ambulance is also removed.
There is now a sponsor by Torgo’s Executive Powder prior to the first commercial break.
Various “minor” bits of scenes, usually with dialogue, are removed and some music is adjusted to fit the re-edit:
There is less lingering on the nudists at the beach.
The scene that first shows the “Box” executives is shortened to less than a second.
Leela isn’t seen giving her credit card number to save pygmy rhinos.
West Johnson Porniversity’s home page isn’t seen, and most of Bender’s dialogue about porn is cut.
Zoidberg says less about his supposed royal relative.
Bender doesn’t announce that he’ll handle Nudar when he shows that Planet Express is now his.
There is less lingering on the office set up in the hangar.
Lars’ estimate on Hermes’ body taking up to a year to fix is gone.
Nudar doesn’t ask Farnsworth to “do more things”.
Amy doesn’t call Nibbler adorable.
The owl’s flight is slightly slower than it is on the DVD.