The biggest difference is that Intel has consulted closely with Christenson, and is not afraid to cannibalize their own market to retain dominance. The Intel Celeron came directly from their consultations with Christenson. The Celeron signficantly dented Intel's profits temporarily but was the beginning of the end for AMD.
And certainly the price is a very significant factor. But remember that ARM sells an order of magnitude more chips than Intel does. So if Intel is successful, they can make it up on volume, at least to a degree.
I dont recall Celeron being a major problem for AMD. The things that did hurt were
a) Intels effectiveness at preventing AMD SKU's from hitting markets
b) The Core 2 family from Intel
c) AMD insisting on shipping 'native' dual / quad cores with worse yields - there wasnt any advantage to the end user and I would imagine the yields were worse
I know, but that was back in Andy Grove's time. I don't think Paul Otellini ever understood the innovator's dilemma that well. In a sense, it does seem like they get it now and try to compete with ARM, but I'm not so sure this came from within the company. I think they were pressured into it by stakeholders and the media a few years ago.
But again, even if they succeeded making competitive chips against ARM, that doesn't equal market success in the mobile market, and it doesn't equal that they will survive unless they take serious steps to survive in a world where they are just one of several companies making chips for devices, and where they might not even have a big market share of that, and where they make low-margin chips. Bottomline is they need to start firing people soon, restructure salaries, and so on. I think this is why Paul Otellini left. He didn't want to be the one to do that, and be blamed for that.
And certainly the price is a very significant factor. But remember that ARM sells an order of magnitude more chips than Intel does. So if Intel is successful, they can make it up on volume, at least to a degree.