I would prefer the X1 Carbon myself, even though it's Intel. I prefer the 14 inch size and without an Aluminium case it's probably lighter than the Z13. The latest gen of X1 uses a U class processor rather than the P-class of the previous generation. I don't know how its battery life compares to the Amd Z13 though.
I opted for a Thinkpad with upgradable RAM recently instead of an X1, as a 3rd party sdimm is about 1/3 the price of the lenovo upgrade.
Lenovo’s choices with U vs. P variants are confusing sometimes. For example, why on earth would you try to cram a hot power hungry P-series CPU into the X1 Nano, a machine with tight size/weight constraints reducing cooling and battery capacity, like they do? Everything about that model screams U series but you can’t build one with that config.
Recently bought an X1 Carbon with a 1270P CPU and had to return it.
In hindsight, the P processor was probably a bad idea, but I assumed if they had it as an option then it would be capable of cooling it. Unfortunately, that was not the case. It was very fast if you only used it for a few minutes from cold, but even just light office use would cause the laptop to warm up until it started to hit thermal throttling, even at only 10%-20% CPU use. Under heavy loads it was even worse, performance dropping to about 20% after 10 mins - equivalent to a desktop CPU from the early 2010s. Sure you don't buy an X1 for building kernels, but you do expect it to be able to handle Zoom screen sharing.
Ultimately, I found that it performed worse under normal usage than the 5 year old X1 Carbon it was intended to replace.
I opted for a Thinkpad with upgradable RAM recently instead of an X1, as a 3rd party sdimm is about 1/3 the price of the lenovo upgrade.