I think there are two ways of interpreting the second sentence.
Audience members participating in the music-making process can enhance the level of engagement and enjoyment for everyone involved.
In one, Audience members participating is the subject, and it means
The participation of audience members in the music-making process can enhance the level of engagement and enjoyment for everyone involved.
In the other one, audience members is the subject, and it means
Audience members who participate in the music-making process can enhance the level of engagement and enjoyment for everyone involved.
The difference is whether it's the audience members who enhance the level of engagement, or whether it's the fact that audience members are participating that enhances the level of engagement. This difference seems minor, but for other sentences with the same sentence structure, it might be quite large.
Intuitively, I would say that the first interpretation is more likely. However, the second interpretation is the one that has the same meaning as the sentence:
Participating audience members in the music-making process can enhance the level of engagement and enjoyment for everyone involved.
So I would say that the OP's two sentences don't quite mean the same thing; or rather, that they only mean the same thing if you construe the first sentence to be the least likely of its two alternative parsings.
If you used involving rather than participating in the OP's sentence:
Involving audience members in the music-making process can enhance the level of engagement and enjoyment for everyone involved,
then it would mean the same thing as my preferred interpretation of the second sentence. But involving is a transitive verb, and participating isn't. This probably accounts for some of the comments claiming that the first sentence is ungrammatical.