To be fair, the Intel post alludes to collaborating with AMD/ARM on mitigating Spectre, but userspace memory leaking is wholly separate from kernel memory leaking (Meltdown, which only affects Intel processors).

It's a developing story, but from the information we have so far, it does look like Intel involving AMD is a disingenuous since AMD processors are not affected by the most serious of the issues.

It's too early to say which is ultimately the most real-world serious.

From the Spectre note (which does affect AMD):

In addition to violating process isolation boundaries using native code, Spectre attacks can also be used to violate browser sandboxing, by mounting them via portable JavaScript code. We wrote a JavaScript program that successfully reads data from the address space of the browser process running it.

How quickly are we going to see attacks targeting BTC/ETH wallets, apps etc. on clients and cloud hosted exchanges?

Hardware wallet or bust right now, right? Use a private key that has never touched the internet?