There are cache architectures (such as pseudo random replacement) that are much more difficult to perform side channel attacks on, but have slightly lower performance.
Intel's problem has been its relentless pursuit of per clock performance, and that has led to some of these side channel attacks. Cache coherency on multi-core is hard.
My guess is that if the market share of Intel and AMD were swapped, you would see similar cache attacks on AMD.
It's worth noting, too, that Intel has diversified-- the processor business is only one very important business to Intel.
Unless you are running untrusted VM from others, you're not making a rational, knowledgeable decision.
Most people are just using this to falsely justify their Intel hate, similar to Microsoft in the 2000s.
Luckily there are other vendors who seem to know what they're doing: We just received our first batch of non-intel servers at work and have no intention of returning to intel for the foreseeable future. What they offer is simply not worth the risk. I expect more companies to follow suit.