I think engineering manager is the easier path to advancement. Compare for example Google Staff Software Engineer (L6) vs Engineering Manager (L6). [1, 2] The latter gets paid more but IMHO the ladder expectations are easier to meet, and even more so when advancing to L7.
This is admittedly cynical, but to some extent I think managers are often judged by the size of their empire, while engineers are judged by their (individual or team) accomplishments, which includes setting the overall project design and filling in gaps between the smaller pieces delegated to other engineers. Building a large empire is easier but can be counterproductive. To accomplish things you also need good design oversight, technical mentorship, etc. that managers aren't expected to deliver.
A lot of people who are passionate enough about software stay on the SWE ladder in spite of the relative difficulty. I know someone who switched to the management ladder then eventually (at great trouble) switched back; he nearly got down-leveled in the process.
There are great engineering managers out there of course, but I think in general the difference in expectations is real and unfortunate.
[1] https://www.levels.fyi/t/software-engineer?countryId=254&mod...
[2] https://www.levels.fyi/?compare=Google,LinkedIn,Facebook&tra...