I really don't know. All his offspring I have experience with were pointed solely at dressage. I know numerous mares have passed their MPT, but I don't think that's really saying much to their jumping ability.
I know of 1 outstanding jumping Royal Prince son: Royal Tribute ridden by Doug Payne. Per Doug's website he is now eventing Prelim. and "In 2009 he was grand champion in the Future Event Horse Series. He won the 2011 5 yr old USEA Young Event Horse Series and was 3rd for USEA horse of the year."
I can't say enough good things about temperament, personality, and overall sweetness. It's hard to walk past a Royal Prince offspring and not give em a cuddle. I would recommend sending an email to Hilltop asking about jumping ability.
I don't know if you would consider using frozen, but Parabol at Hilltop Farm also has some sweet babies and lots of offspring competing in Hunters/Jumpers and eventing. I think Parabol himself might have been a jumper at one point? May be worth asking Hilltop about him too?
I owned a Royal Prince youngster that was crossed with a Wallstreet Kid mare. I bought him as a unbroken 2 y/o. He was/is fancy, fancy, fancy. Had a walk like a panther that just made me smile. He was sold as a late 5 y/o as a amateur hunter. He has a great mind and a fabulous jump. If you would like to see pictures, send me your e-mail via pm and I would be happy to forward you some.