1. How much value is there if it goes right?
2. How easy it is to get right?
3. How gracefully will it break down if it's not done perfectly?
Methodologies don't have to shine on 2 or 3. NASA-style clean-room coding is the gold standard of hard-but-effective; you have to suck it up and commit entirely with a great team, but the results are unbeatable. Waterfall was "good, bad, bad", but used by lots of less-exceptional teams with hideous results.
Agile, I think, improved #3, but not #2 so much. It's commonly sold by appealing to how much it can potentially help, but I think the more honest pitch is "it's tough to do right and it'll sting if we get it wrong, but it hurts a lot less than getting waterfall wrong."
I know such a simple rule is probably causing a lot of you to cringe, but I can very easily fit just about any activity of value you or your team embarks on into that question, and it's a rule the entire company can get behind.