A 76 Les Paul will have a pancake body, a 3 piece maple neck, an ebony board, larger headstock with volute.
The 94 will have a weight relieved body of mahogany with no crossbanding, a 1 piece mahogany neck, rosewood fretboard.
So the guitars, from a construction point of view, are about as different as 2 Les Pauls have ever been in the whole history of the guitar......
As you've found yourself from experience, and from replies there can be a variation in instruments. But typically you still get the tone of the instrument you bought. If they are way apart maybe there is an electrical/wiring issue at the heart of the difference.
Also so far you have not said specifically how the two guitars differ tonally, and how that somehow becomes 'unusable' from a live point of view. Lets face it, plenty of people rely on singlecoil Fenders as backup guitars to Les Pauls and will happily substitute the two.
Unless you're Brian May who relies heavily on the unique tones from a specific electronic setup......or your audience want to hear play cover songs dead on to the original, surely a slightly different tone isn't going to make whatever audience you play to suddenly think they're not getting the entertainment they want.
