In this case, I would like to see the shock troopers doing what they do, and have the event of chasing Ahsoka Tano be depicted from the point of view of the troopers plus the fugitive's master himself (Anakin Skywalker). After their brief fight with Ahsoka and Asajj (https://www.youtube.com/watch?v=fXvi3i25HZg), they get a quick breifing in the gunship, (and for comedic relief/comic relif,) are shown some other pictures of Ahsoka to get her appearance better set in their minds, and it just happens that those pictures not only include the season 1, 2 and 3 1/2 Ahsoka (yes, I admit, I liked the older appearance better, not that I have any problems with the newer appearance,), but also, some pictures that, let's just say, Anakin or Ahsoka wouldn't be particularly enthusiastic about the entire universe seeing those (a reference to what happened in Meet the Spy).
By the way, if I was in either Ahsoka's or Asajj's place, I would've picked up at least 1 blaster to both give me a ranged and less-than-lethal (with "stun" setting) option.
I'm also surprised that none of the troopers managed to shoot either Ahsoka or Asajj, especially with their fingers on the trigger the whole time (which is terribly unprofessional, irresponsible and outright dangerous, and is also demonstrated in many movies, tv shows, videogames, etc). The only logical reason that I can come up with is that the troopers didn't want to shoot any of their teammates in such close range and that chaotic of a situation. Even though they probably wouldn't die (assuming that their blasters are set to "stun" and none of their assailants attempt for do further harm to any of the troopers), it is not good to have a teammate knocked out of action.
I have more criques like the one above in "A few parallels between Star Wars & the New World Order, how Barriss stayed in the Jedi order, & more", and "Trivia post: Star Wars: is Anakin Skywalker good or evil, Anakin's Clones & Rise of the droids & how Shaak Ti could've defeated Grievous".
Why do stormtroopers miss so much?