They do exactly the same thing, they upvote posts/comments with dust, above the $0.02 threshold. What differs is the way you activate each service.
For @dustsweeper you have to transfer steem/sbd and keep an active balance, this balance is used when Dustsweeper votes. The amount subtracted from your balance equals the amount you receive as author rewards. So your profit is purely the dust votes, that otherwise would have been lost.
For @dustbunny there is both a free version and a paid/VIP version. By delegating SP to Dustbunny you achieve a higher status and will receive more votes. For the free version, you can just make a comment on a recent Dustbunny post asking to be added to the list.
Even though they do the same thing, they complement each other very well. Both services will never vote on the same post as the first service to vote will push the value above $0.02 and then it will be skipped by the other.