Willys powered gennys are fairly common and usually the engines make good transplants since running a genny is easy duty. However, if the engine sat in the weather, uncovered, then it's no better than any other Willys engine that sat out. While the basic engine is the same there are some differences. The intake manifold and carb are almost always different and need to be replaced. If it has a head marked "Industrial" that is a lower compression head and should be replaced. In some instances the pullys can be different which would also require replacement. The good news is that all of that from the old engine will bolt right on. By the way, the designation for the Willys powered genny was PE-95.
Maybe Bob W will jump in here. I don't recollect seeing that type of water-proof ignition on a genny before and what the heck is that do-dad on the right front? Looks like a pressure regulator of some kind right where the oil filter would be.
Larry