Prophetstown is relatively new, so not a lot of shade. Very nice, big park with trails, riding paths, and a historical, working farm. Fhu sites, and electric only sites are carved out of the prairie. They are open; fhu sites a bit more secluded. Tippecanoe is an older, established park with mature trees and good shade. Huge, again with hiking paths and biking. In season, sandhill crane gathering ground is nearby. Thousands of them flock there. Another nice park, nice facilities. Outer loop of campground offers more space; inner loop seems a bit crowded. Have not been to chain of lakes.
Ps: big weekend festival in Lafayette first weekend of October, so check the Prophetstown site for availability.
http://indianastateparks.reserveamerica.com/