The HX35 that came on the '95-'02 Cummins trucks was a derivative of the H1C that we got on the 1st gen and '94model year 2nd Gen trucks. The '94 got a WH1C which is a ("W" meaning wastegated) and I believe it was in '95 that Holset changed the way they identified their turbos. After that the H1C/WH1C was known as a HX35.
The main difference between the H1C and the HX35 is the compressor housing. The HX has a smaller housing which allows it to spool up much quicker and therefore it will perform better. You can go to a vendor such as Pier's Diesel and get a smaller compressor housing for about $175 and get the same results as swapping out to a HX35. It has been suggested that unless you're running real high HP then the smaller the housing the better. For reference the HX35 has a 12 cm2 housing whereas our H1Cs have an 18-21 cm2 housing depending on year.
For more information see this page:
http://dodgeram.org/tech/dsl/FAQ/turbo_faq.htm