At the pure tech level it's not equivalent. One required the ability to cut and paste and be done in a few moments, the other requires you to implement your own interface against the REST interface.
For a drop-in replacement, although not open source, I think moot.it looks pretty good: https://moot.it/
They're aiming at the embeddable market for comments and forums and have a pretty nice product.
Discourse is of course good on the open source side, but unless someone can point me at a JavaScript tool to allow embedding as simply as Disqus or Moot.it I think it's not the best match for this scenario.
As always... what's the full use-case? What are they trying to achieve? What are the priorities guiding the decision making process?
Discourse wins if the important criteria here is open source and the person asking the question is fine implementing the integration using the REST API.
Moot.it wins if you just want a drop-in replacement and that trumps the open source.
Writing your own wins if you want a project that will take far longer than you anticipate :)