It's not just about Intel vs AMD, but a whole different design philosophy.
Comparing the Lenovo ThinkPad Nano vs the HP EliteBook 845 G7 (check the full review) is not an easy task, but as ultra-books they both target the same audience, with huge differences in their main goal.
While the main goal of the ThinkPad Nano is being as lightweight and small as possible, HP goes a slightly different direction and targets power users, who require performance in a lightweight package. So why compare them anyway? For me both machines are clearly the best at their respective class and depending on your use case they are both a great pick.
Both are extremely well manufactured devices. Personally I prefer the all black Lenovo Magnesium Body over the silver HP aluminum one, not for the looks, but the feeling while carrying it or typing on it. The HP EliteBook has some sharp edges and especially when using on the lap can feel a bit uncomfortable compare to the Lenovo.
The HP keyboard is more sturdy and you can feel that HP used the space wisely. Sadly it has not that "Lenovo / IBM" feeling, but is still great for typing long texts. The Lenovo keyboard on the X1 Nano only has 1.35 mm key travel, which you can feel compared to the HP one, but it's still awesome for typing. The tactile feedback is different on both, space between keys is larger on the HP keyboard. They both got the integrated mouse bumper and have a top-side click pads.
Glas-like feel on the HP side, more usual plastic feeling on the Lenovo. Personally I prefer the Lenovo one, but both are doing fine and you can always switch to the Track Point on both devices (where the Lenovo one feels slightly better too).
While the X1 is clearly the better Couch laptop, the HP does a great job as an ultraportable notebook too. The alumium case does not feel as good as the Lenovo magnesium one, but the better performance and maintenance (!) make the HP the overall better value. The HP has no Thunderbolt 3, but 2 DisplayPort USB-C and one HDMI 2.0 port. Additionally it has two comes with two conventional USB-A 3.2 ports, so you don't need to carry a Dongle all the time.
Both work great with Linux, with a slight advantage for the Lenovo in terms of power savings and compatbility.