TB x ID was the traditional ISH, although it could be only 1/8ID, but now it covers a much wider range of crosses which often includes warmbloods. This is to a degree that in Ireland the IDxTB and ConnemaraxTB is now called a Traditioonal Irish Sports Horse to differentiate between them and the warmblood crosses.
My experience of IDxTBs is that they usually combine the best traits of both breeds, though that said I'd go for a good RID every time and work around their tendency to think they know best - at least if you get them into a mess they have the power, brain and athleticism to get you out of it again - simply because I love the honesty and generosity of the breed. The cross keeps that to a degree, but it isn't the same. The cross is an easier ride though as it almost never has the power of the purebred, and it can be easier to train as the mindset is more flexible yet there isn't the reactivity that's often associated with a pure TB and the build is tougher.
All the ConniexTBs I've known have been cracking little horses - tough, fun, sane.