The other part is that Engineering Manager is a terminal position, I've known a few people who were manager for 20 years without ever going to Director / Exec whatever, its just a competitive jump and mathematically most will never go up. This is ALSO true for Senior -> Staff and Principle though. But Engineering Manager positions often have more of an upside with bonuses / incentives than Engineers get.
Finally it is ultimately a career change, and that should be the primary factor to consider.