i play both extensively, (Reinhardt is my one true-love, golden hammer/axe + probably over 50 hours on him + about 20+ hours on Orisa), Reinhardt is more mobile and does more close-range damage, he's great on attack for 2cp and escort/payload maps because you can initiate attacks with him.
Orisa is more situational and better use on control point depending on the team comps. She also has the advantage of being able to walk away from her shield and i feel like over time her shield takes more damage then Reinhardt because of lower cool-down and bigger barrier (it recently got buffed). Orisa also has the functionality of being a long-range tank so if you have no long-range DPS she is very useful + she can take out Pharahs.
In a 1v1 battle a good Orisa should always counter Reinhardt though. just bait out his charge, Fortify and shoot his head.