The version on Hulu does not seem to be cut for content, but it does have some minor alterations to its opening animation.
Trigun was originally dubbed and released by Pioneer pretty much intact. The one exception: in the Japanese version, the opening animation would show different characters, while the original Pioneer release used the animation from the first episode for every episode, so the Episode 1 villain keeps appearing long after he's gone from the show. From the Anime News Network entry on Trigun:
The initial region 1 version of Trigun released by Pioneer/Geneon (original Pioneer and Geneon Signature Series) did not include unique opening animations for each episode as did the Japanese release of the series. The first episode's opening animation was used for the entire series in the US domestic release, while normally, the opening animation highligted characters present in the particular episode that was playing. Geneon's latest release of Trigun (Limited Collector's Sets 1 & 2) has restored each unique opening animation to its original state.
Geneon later folded and lost the license to Trigun. It was picked up by Funimation, whose release is the one playing on Hulu. From a review of the Funimation DVD release on Anime News Network:
Funimation's boxed set rerelease is apparently taken from the original Geneon/Pioneer releases rather than the later Limited Collector's Set releases, so fans looking for the openers as they originally played in the Japanese broadcast – i.e. with slight adjustments to the animation each time to reflect characters featured in that episode – will be disappointed. Instead, Episode 1's opener repeats throughout.
I watched bits of a few episodes to confirm that the dub is the same, and that the same opening animation seems to appear in Episodes 1 and 2.
Trigun was also shown on Cartoon Network, where it was edited for content. At the time, Anime News Network had a feature called The Edit List where they tracked cuts to anime airing on TV. The Trigun episodes are spread across April 2003 and May 2003. I checked on a few of these scenes and confirmed that the uncut version is what's on Hulu. For example, from Episode 1:
2) Boss's "You asshole! What the hell do you thing [sic] you're aiming at?" changed to "What the hell do you think you're aiming at?"
This happens around the 13:15 mark in Episode 1, and the Boss does indeed say "You asshole!".
It's possible that Funimation cut the series when they did their DVD release, but it seems unlikely, especially for a show like Trigun that attracts an older audience. The choppiness probably comes from the fact the Trigun is not an amazingly well directed show. The art direction of the show was mediocre even at the time it was released and has aged very poorly compared to shows like Cowboy Bebop and Evangelion. I remember scene transitions and camera changes often feeling abrupt. The writing also has its flaws, mostly from the usual cause of trying to cram too much manga story into too little anime. That's probably enough to account for that disjointed feeling.