The objective metrics are things like: transistors per square millimetre, power per billion transistors, frequency, SRAM bit-cell size, etc...
Marketing calls it "7nm+++super", engineers get graphs of power-vs-frequency.
E.g.: comparing transistor densities:
Intel 14nm 38 MTr/mm^2
TSMC 7nm 97 MTr/mm^2
Intel 10nm 100 MTr/mm^2
Samsung 5nm 127 MTr/mm^2
TSMC 5nm 173 MTr/mm^2
Intel 7nm "higher than TSMC 5nm" (planned for 2022)
TSMC 3nm 290 MTr/mm^2 (risk production in 2021)
This should make it pretty clear why Intel is going to struggle to be competitive: The majority of their products are stuck on 14nm, which has 22% of the transistor density of TSMC's bleeding edge product. They can't compete with the likes of AMD and Apple with such outdated tech.
It should also make it clear that Intel's 10nm node is basically the same as TSMC's 7nm.
However, from what I heard (I'm not an expert!), Intel's 10nm node is a "pain in the ass" to manufacture. The design phase is complex, the yields are low, etc...
For comparison, TSMC's 7nm is supposed to be a relatively "straightforward" process, and 5nm is actually an improvement in manufacturability. That is, it's easier to design and make a 5nm TSMC chip than a 7nm TSMC chip. That's actually a pretty big advantage, something Intel doesn't talk about much...