Re: different ways of applying kotegaeshi
Each technique has multiple variations. In some cases, the variations emerge from differing assumptions with regard to the reality.
Without going to detail, I would go for the Aikido version, it sounds more similar to the one we use. While If I understand the IRT grab you described, you only have both thumbs on the back of the hand (I have seen this variation in some other M.A.).
The advantages of the aikido variation as we use it are:
-> Your "other hand" can apply more pressure. Full hand is much stronger then thumb.
-> Your "other hand" can shift to deflect slaps more easily.
-> Your ability to shift techniques if the situation varies is increased.
Then again, perhaps I misunderstood your meaning in one of the descriptions and my explanation is moot :-(