Hardware

Security including but not limited to:
Spectre:
https://en.wikipedia.org/wiki/Spectre_(security_vulnerability)
Meltdown:
https://en.wikipedia.org/wiki/Meltdown_(security_vulnerability)
Downfall:
https://en.wikipedia.org/wiki/Downfall_(security_vulnerability)

These issues stem from several areas of CPU optimizations, Unsafe Branch prediction, multi-threading, and memory optimizations. While some AMD CPU's were somewhat touched by spectre/meltdown, they could be patched pretty easily, while Intel was hit for several complete generations of CPU's, and patches caused speed decreases of sometimes 30%.

Stability:
Several issues with overheating:
https://www.youtube.com/watch?v=-kxlrez5dWo

Unclear guidelines for CPU setup:
https://www.pcgamer.com/hardware/processors/intel-pressures-all-motherboard-manufacturers-to-implement-default-power-settings-by-the-end-of-may/
This widespread malpractice caused unsafe and power hungry OC to be default on many motherboards.

Compatibility: There were compatibility problems with crashes when Intel introduced e-cores, where the solution was to disable e-cores. Unfortunately this problem is apparently now drowned out by newer problems with Intel CPU's, so I can't easily find sources.

In most cases these problems are not total killers, but they often cause the CPU not to perform as advertised. And they do cause occasional crashes, as we could see in the video, way more often with Intel than AMD for the past 2 generations, but there were also problems with 12th gen. and AFAIK with almost every gen since Kaby Lake (Spectre Meltdown).

This is a massive issue seen over time, so I have probably left things that are significant out. I have left out things that go too far back on purpose, because I don't consider them relevant anymore, everything before Core2 is irrelevant now IMO.