The no layoffs during a downturn was not really what was communicated to anyone looking for a job. Maybe in upstream? But that is a dumb fallacy to believe especially given that COVID market conditions approach the mass layoffs in the 80s (nothing this major has happened since the 80s). And to be fair, in 2015, while all competitors were laying off thousands of their upstream engineers, exxonmobil moved many of theirs into their downstream business lines to prevent layoffs.
Exxonmobil starting salary (at least for ChemE in downstream) was nearly on par with compitition for the way it was structured so long as the market was doing well. EM has a higher base salary versus competitor lower base salary + bonus for company performance + bonus for personal performance. When the times are good, competitor can potentially walk away with more salary for a given year. When times are bad, not so much. EM sells on a more stable salary year-over-year.
What I have seen around 2015 was that EM would hire fresh grads in the $90k range. Competitors would hire in the mid $80s with potential for up to 10% bonus (5% made up from company performance, 5% from personal). On average, with 5% bonus, the companies pay would be roughly equal EM. Other companies also rank their employees on performance (similar to us), so there are very few people that actually get the full personal bonus %.
What's true for almost every company though, staying with the same company will see your raises stagnate versus if you go to other companies. This is true even if you work at a competitors company long term also.