I've seen a few Rapport offspring. The ones I've seen, have been doing dressage, but I've heard some are also talented in the hunter rings. The one's I've seen at shows, all seem to have a great work ethic. I believe a few of his offspring have made it to the Grand Prix level, one being a mare named Rannoch.
I have a rappheal filly which is one of rapport's son's. i can say that she is one of the easiest babies i have ever come in contact with. (stands on a trailer by herself after her travel compainon left with her hind foot cocked munching on hay. love her! My filly/mare is 3.5y'o and i hop on her every now and again in a halter and lead (sometimes just a halter) just to walk around and "pony proof" her. she will pretty much do whatever you ask. she is super atheletic and free jumps great, looking forward to officially breaking her this spring.
We have a Rapport mare in our broodmare band. She is very quiet and super loving, but is more the sensitive type apparently under saddle. She seemed to have a great work ethic, probably to a fault - was pushed and fried a bit by her previous owner. Very much the pleaser type that worries. Supposedly she has great talent for piaffe and passage. I am sure she could be started again slowly with someone who praises her often that she trusts and be fine, but she's been such a good broodie that we haven't desired to go that route. She also likes to jump! (will jump fences in the ring at liberty) Very protective of her herd, a care-taker type. She has produced foals with great temperaments that have beautiful heads, necks and toplines.