Amaterasu hits kakashi, Kamui hits itachi. Itachi likely dies from kamui, thoughi he may live if he gets hit in non vitals. Amaterasu burns kakashi. Kakashi uses kamui on amaterasu. Kakashi lives but is badly burnt.
Kamui can't warp ametarasu before it gets to Kakashi, as amaterasu spawns on its target.
How is Kamui going to warp Amaterasu when Amaterasu cannot be seen until it hits it's target??? Itachi gets his head sniped off Kakashi get his head burned...
Well kamui isn't instant on impact, it still takes time to warp the target, amaterasu is faster and would disrupt kamui from kakashi use however obito's use is different and he would get hit by it but would be able to warp it away.
If Kakashi doesn't react fast enough, which is quite likely, Amaterasu gets him. If he does they just stalemate, but Itachi/Sasuke could use Amaterasu more consistently than Kakashi can use Kamui since he has less stamina/chakra + Kamui uses more chakra.
Amaterasu hits directly that point which is targeted by the user.
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Kakashi would die in that case. Obito had to use his final trump-card, Izanagi, to survive Tenshafuin: Amaterasu.
Amaterasu is even faster than Kakashis Kamui, because Kakashi has to build up more chakra, before he can set the Kekkai for Kamui.
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However, they could kill each other with these Dōjutsu, without a question. But the possibility to avoid Kakashis Kamui is higher than Amaterasu, because the way of functioning is different. Amaterasu comes to life on the target(that's why Sasuke could use it inside Susanoo) and Kakashi has first to build a Kekkai and in the centre of these Kekkai the space will distort.
Gedō Mazōs head was targeted but it could escape due to Madaras Kuchiyose no Jutsu(Kamui hit the arm though)
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Deidara stir out of Kamuis Kekkai too. Both cases are similar.