Many cats are suspicious of changes they can't control, including menu changes.
I generally tended to keep the same kibble for long periods unless there was a medical need for a change, offering a variety by mixing up the treats. With the most recent pair, wet food was mostly considered a treat, since they liked gravy but were only slightly more interested in the meat pieces that in their kibble.
As far as I could tell, they found the stable diet comforting rather than boring.
The easiest way to introduce a new food is to present it alongside the previous food, wait until you see the cat eating it (ideally, preferring it), and then phase out the prior food if you want to do so. That isn't always possible if you are moving them to a food that is better for them but that they don't like as much; in that case you may need to start progressively offering less of "the good stuff" to get the cat hungry enough to eat the new diet.
Regarding cats vomiting when they try new food: they may have an allergy... or they made just coincidentally hack up a hairball after trying the new food. I wouldn't rush to associate the two unless it happens every time the cat tries the new diet.
My vet: "Any vomiting?"
Me: "Not more than usual for a cat."