I think you'll find it's a mixed bag. For me I can say that my experiences in originals bands have greatly informed what I do and what I think about music in general, and some of that leaks out in how I approach doing covers. The way audiences react to the unfamiliar, for example, is an important thing to understand when doing both sorts of bands, but it informs planning for each in different ways. And so on.
On the converse, the way I approach doing original music is also well-informed. I still write it, I still produce it, but I don't perform it for a variety of reasons. There are circumstances where I might, but I haven't leaned into that sort of situation lately because it would be difficult to create and sustain to my own satisfaction.
What many people in both situations don't realize is that it's important to craft an experience for your audience that they will relate to in some way and cannot get elsewhere. If you can't write catchy songs that will grab an audience as though they've been heard before, you're going to have a more uphill battle getting audiences familiar with your music. And, in general, it's a different audience.
Covers tend to appeal to people who like to go out, whereas original music might be a serious destination event for people. In other words, the people who go out to see cover bands are going out frequently and looking for the most fun musical experience they can find, whereas the people who go to see original music might only go out once or twice a year to see their favorite bands because they liked what they heard on Spotify or Pandora. It's much harder to get those people out. On the other side of that coin, if you can get the attention of those people and they really, really love you, they'll follow you around relentlessly. And that's true for both covers and originals.
These things, of course, are true in my own experience with the kinds of bands I've been in, but may not be relatable in other genres or regions. My cover band makes a point to give people a unique experience that isn't gimmicky but is something they can't get elsewhere, and whenever we play we receive a ton of good feedback on those aspects because we've planned it that way. I probably would not have had the insight to plan things that way had I not experienced audiences from both sides of the live music world. All of that has helped me understand what audiences are motivated by.