I've used both.
The shuns where higher HRC on the steel and either vg-10 (comparable to BDZ1) or SG1 (much better than BDZ1) depending on if they are normal or "elite" lines of the Onion-designed Shun series. The Shuns are also san-mai or laminate construction meaning that a thin layer over very hard steel is clad on both sides by softer protective steel (the 3 layers are forged together and will not separate). This allows the actually steel doing the cutting to be harder (last longer) without making that over-all blade too fragile/ brittle. More importantly it makes both sharpening and thinning behind the edge (as needed on any knife over time) MUCH easier. The Rains are mono steel (no cladding). That means if you've got A LOT over very difficult to grind metal to chew through if want to thin or sharpen them. This apparently is plus to folks that think that a home chef might wear a knife out in a couple years because they plan to attack them with a 3hp bench-grinder, coarse wheel, and determined ignorance.
The handle materials on the Shuns is their own version of "pakkawood" which is a wood that has been impregnated by resin under high heat /pressure in order to stabilize it. The Rain's G10 is a full synthetic material that's very popular in non-kitchen knives but not seen much in the kitchen. The Shun's are already proven to be very durable in the kitchen, but g10 is also a very tough material.
The only possible issue that I could see is that any time you have a sandwich of handle-tang-handle material they will expand /contract at different rates and over time, gaps may form between tang and scale (especially when there are only 2 rivets on the handle and you think that knives should go in the dishwasher like Cpt. smallbit: blind defender of all things Onion). But as long as they arn't abused / exposed to dramatic temperature changes, they should be fine.
The big difference between the "Shunions" and the Onion Rains are that one line was made by Shun and the blades ground with proper full contour and thinness behind the edge and the others are made by Lamson&Goodnow who ground them very flat and as over-thick as some people's skulls behind the edge.
Both have the same "signature" clueless anti-ergonomics that most intelligent users will realize is mediocre for some and terrible for others.