If you’re willing to leave, then there’s no downside in using your offer to negotiate. Just do it gracefully. “I don’t really want to leave, but 20% in a growth industry ...” see what they come back with. If nothing else, it’s excellent practice for when this situation may arise again for you in the future.
Having said that, it’s very unlikely they will be able to do much. Exxon HR systems are built around the idea they are a top tier company that has no trouble attracting elite talent. Salaries are set by HR, they follow directly from ranking, and that’s it. your boss (and boss’ boss, and boss’ boss’ boss) literally has zero ability to bump your salary outside of ranking. They can go ask HR, and HR might offer some flexibility to give you a bump. But 20% would be extremely unlikely. It wasn’t until I was a CL29 that I was able to give directives to HR on things like salary in situations like this, and even thenHR has limited flexibility, and beyond that they’ll say it takes DOAG 4 (president) to approve anything beyond (will never happen).
And even if you do get a salary bump short term, Exxon will claw it back over the next several years by allowing your salary to regress back to the salary curve.
Where managers have more ability to influence is on next role, so maybe you can negotiate a promotion to next level out of it. But even then very few managers have a clean +1 CL role ready and waiting. Your next role is usually a negotiation between your manager and the manager in the receiving org. And depending on your level, often those things are managed at your manager +1 level.
This is all a long way of saying, if you’re willing and ready to move on to AWS, then your best move is to gracefully, “more in sorrow than in anger” ask your manager what he can do to make it easy for you to stay. The result will likely be you go to AWS, but treat it as an opportunity to practice this type of negotiation. You’ll probably learn something useful to you later on in your career.
Enjoy AWS!