My answer has more to do with film than history, I throw myself on the mercy of the mods if it's not within the idiom of the sub.

I can think of a few things the advent of film changed about puppetry, at least when the two forms meet. To demonstrate, I shall use my personal favorite puppet-related entity, The Muppets!

cue Can You Picture That?

Oh yeah.

First, the camera frame. On stage, if you want to keep your puppeteers invisible to maintain the illusion that puppet characters are "real," you have to very carefully hide the puppeteers on or underneath the stage. In film, though, your stage is effectively whatever the camera can see. By playing around with perspective, you can shoot scenes with puppets even in places like an open field, and never see the puppeteers. On a smaller scale, you can have a puppet character interact with a human character without the puppet having to sit on a desk or something else the puppeteer can hide behind: Just shoot them both from the waist up, and it looks like Kermit is standing there talking to Zero Mostel.

Second, on a more technical level, cameras gave puppeteers an invaluable tool: The monitor. When shooting, Muppeteers can see whatever the camera sees on a small screen that's placed down in the "trenches" with them. Not only does this let them ensure that Kermit appears to be looking Zero in the face when they're speaking, it also lets them see body language and other small visual cues, allowing for superior timing and more realistic reactions on the part of the puppeteer. This is part of what makes Muppet characters feel so "alive." It also allows for superior coordination when two people are required to run one puppet, like the Swedish Chef. The Chef is, in fact, one person running the mouth and head, while the other acts as the arms. The original Chef team was Jim Henson (head) and Frank "Yoda" Oz (arms), actually. Next time you watch a Swedish Chef bit, notice that when he does something with his hands, he tends to look down at them. Then think about how hard that would be to accomplish if the two puppeteers couldn't see what the audience sees in real time.

Last, special effects. If you've seen The Muppet Movie, you probably remember the famous scene with Kermit riding a bicycle. It was an impressive accomplishment in '79, even if it only worked a couple of times. But that's just it: It only had to work a couple of times. If it were tried in a stage show, it would have to work reliably well every single night, maybe multiple times a night. With film, it only has to work enough times to get a good take. It seems simple, yes, but I got such a sense of wonder as a kid when I saw Kermit riding a bike, apparently under his own power.

I hope that was helpful and interesting, if nothing else I appreciate you giving me the chance to talk about Muppets! That always brightens my day.