Looking at the latest in the ARM landscape, we have Apple A9, Qualcomm Kryo, ARM A57, ARM A72, and AMD A12. We can probably expect a small jump in Apple's performance next year along with a second revision of Kryo, but nothing competitive with Intel. A57 is being dropped for the fixed A72 since Apple screwed over ARM (tl;dr Apple shipped a new architecture in 2 years while ARM took almost 4 years for an inferior product -- everyone in the industry knows that design to shipping a new architecture is 4-5 years indicating either ARM screwed over all their non-apple partners (and themselves) by giving Apple a head start or Apple forced ARM to adopt a new ISA when they'd already had a couple years to work on int). Of all these architectures, I think only A72, AMD's A57 implementation, and AMD's A12 are worth focusing on.
A72 is supposedly close to the performance of Intel's core M processors, but I'm willing to bet that the default A72 can't actually compete with Skylake's wide dispatch, SMT, and vector units. The biggest question in this area isn't actually the CPU so much as all the "uncore" parts surrounding it. Even if it could have these things in theory, the companies controlling most of the patents in this area aren't using the A72 (AMD, Intel, IBM, Oracle, etc).
AMD's first generation of ARM processor (launching next year) is an A57 server part, but is probably going to be faster than most A72s in practice because it can be manufactured on a high-performance (rather than bulk) fab process and will have faster buses, faster memory, much larger caches, and even some parts of the core (like the branch predictor) may well be replaced with better systems while AMD's reworking the entire architecture for the new fab. This chip will probably be competitive in the low-power server market, but most likely won't be aimed at anything mobile.
Not much is known about AMD's A12, but for the first time, an ARM company seems to be moving into the higher-performance mobile segment. AMD failed with bulldozer (and has taken the heat for beating that dead horse for the past few years), but they at least had the sense to hire Jim Keller to help them make a couple new, next-gen architectures. While AMD has money troubles, it's in the intellectual property sweet spot to be able to put together a competitive chip. This is the chip I think Linus is wanting, but it's been pushed to 2017.
The complete unknown is Intel. They bought DEC and StrongARM was along for the ride, but they sold it in '97. They then made XScale only to sell it to Marvell in '06. I find it hard to believe that Intel's not experimenting with ARM design again. Even if they could make x86 compete in the low-end (atom has been a failure in that regard), convincing companies to switch will probably prove impossible as the current situation with lots of competing CPU providers works to their fiscal advantage. Apple won't be giving up the freedom to make their own chips (nor will Samsung). That said, I don't think we'll be seeing an Intel ARM chip before 2018-19.
tl;dr -- the current chips can't compete with Intel. The ones that can don't launch until 2017 or later.