I thinking about building a recurve or maybe a longbow from a Bingham kit. Is there a performance advantage to using the 2in limbs vs the 1 3/4in limbs in the recurve and the same question for the respective longbow limb widths?

I don't think there is any advantage to using the 2" width, I don't really have a reason I have just always used 1 3/4" for most recurves and 1 1/2" for the longbows.  I know that doesn't really answer your question.  If 2" had an advantage we would have seen a bunch of bows built with it.  
Come to think of it it would take more material to make the same weight when using the wide stuff.  Remember double the width double the draw weight double the thickness the draw weight increses  eigth times.  Therefore less mass to get the same weigth, better performance.  Probably very little gain but some.

I asked the same question last year..Jess is right about stack ..for 55#s you can build a limb with less mass using the 1 3/4" glass than the 2" glass..the reason is that the thicker stack builds more draw weight than the wider thinner stack of the 2" glass. Look at the weight chart on Binghams web site and do the math

I have only ever used 1.5" glass for both longbows and recurves. Can't imagine using wider glass.

Whatever width you choose for a recurve, Bingham's limb kits will have the appropriate stack thickness to get you very close to your desired draw weight as long as you follow their design.

Thickness adds more draw weight than width,at about a 3 to 1 ratio, so theoretically a thicker, narrower bow of the same draw weight and some material will shoot a little faster than a wider thinner bow of the same draw weight and material, however a wider bow will give a little more stability, or resistance to limb twist, especially in a highly reflexed or recurved design, that's why most longbows are 1.5 and recurves 1.75. After tillering longbows usually end up around 1.25 and recurves 1.5.