What are the differences in benefits under Admiralty Law and regular State Law, assuming my accident happened on the job?
There are very significant differences in benefits, the most dramatic of which is that a direct damages lawsuit is authorized for a member of a crew of a vessel against his or her employer and, under most State's Laws, any remedy against an employer is limited to Workers' Compensation Benefits.

If I'm hurt on a barge being towed on one of the Inland Rivers, such as the Arkansas, the Tenn-Tom Waterway, The Mississippi, etc., do my rights fall under Admiralty Law?
Yes.

If I'm hurt on an offshore drilling rig out in the Gulf of Mexico, or in an inland bay of the Gulf Coast, do my rights fall under Admiralty Law?
The answer to this question depends entirely on the exact type of rig on which you were injured; Admiralty Law would conver certain types of rigs, such as Inland Barge Rigs, Jack-up Rigs, Semi-Submersible Rigs, etc. However, it would not apply to many other rigs, such as Fixed Platform Rigs, for example.

Would Admiralty Law apply if an accident occurred involving a pleasure craft, such as, for example, a group of friends out fishing or sailing, or personal watercraft such as "Waverunners"?
In general, the answer is yes, although the legal classification of the various persons involved in any given situation, such as, for example, the fishing trip, would depend on the exact facts of each case.