The two most promising Islamic State AUMFs I have seen are the one sponsored by Representative Schiff and the one sponsored by Senator Kaine. Both drafts, in different ways, purport to limit the authorization for the President to use force against the Islamic State in at least three respects: (1) They authorize force only in Iraq and Syria, (2) They do not authorize ground troops (except for training or rescue situations, and the like), and (3) They do not authorize force against associated forces (though Kaine’s does if a certain report is filed).
The draft AUMFs appear to be entirely ineffective in limiting congressional authorization to use force against the Islamic State in these three respects. The reason is that the limitations in the draft AUMFs, by their terms, apply only to the specific authorizations in the draft AUMFs. They do not affect Congress's authorization of force under the 2001 AUMF. The Obama administration interprets the 2001 AUMF as an independent authorization of force against the Islamic State, and the 2001 AUMF does not contain any of the limitations. Assume that one of the draft AUMFs becomes law. If the President decides that he wants to use ground troops in combat against the Islamic State, or that he wants to use force against Islamic State in Lebanon, or that he wants to go after forces associated with the Islamic State, he can simply choose to base his action on the 2001 AUMF. And he could still maintain that Congress authorized the action despite the newer AUMFs.
If Congress wants to limit its authorization of force as applied to the Islamic State concerning geography, ground troops, and associated forces, it must also specifically amend the 2001 AUMF to make plain that the 2001 AUMF itself does not authorize force against the Islamic State outside of Iraq and Syria, or against associated forces of the Islamic State, or involving ground troops against the Islamic State. (I note that the Schiff AUMF sunsets the 2001 AUMF after 18 months, and thus would eliminate all independent authorizations under the 2001 AUMF 18 months after the new Islamic State AUMF comes in to force.)