As someone who is going to eventually become a liscenced professional engineer (graduating this semester, then I'll have to go through a few years as an EIT), and looking into specializing into structural engineering (and hopefully later, bridge design)?
Integrity, hands down.
Yes, professionalism is a factor here. To have such a status held in such high regard and having an enormous amount of responsibility means that it's actually in my best interests to maintain my integrity, having a reputation for honesty is a necessity for my chosen profession. Even I don't do anything technically not illegal, I could easily lose my liscence for such conduct and be banned from practicing engineering as a result.
To put the situation into context... everything else being equal, who would you rather have designing a major bridge project? An average person with a reputation for integrity, or a rich person who's rumoured to be a sell-out? Who would you trust?
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Unlike many of you, it's almost certain I'm going to run into this sort of situation over the course of my career; not just once or twice either, repeatedly. Willful neglect and cutting corners are not an option for me, I have to ensure that anything I design is both functional and safe. I have a duty to society as a whole to do my work properly, and it can't be comprimised for personal gain. Suggesting cheaper alternatives (which are still viable) and genuine improvements are acceptable, but a certain standard must never be comprimised.
On the bright side, my chosen career path does more or less guarantee a substantial salary. Nothing outrageous, but I should never have financial issues due to a lack of income; overspending and other expenses can still cause problems, but that's a different issue altogether.
Considering that many of the projects I'll eventually are guaranteed to have multi-million dollar budgets, if not multi-billion? I'll have to make sure whatever is built is built right; and for people to allow me to do that, they have to be able to trust me with all that money. And they will be watching. Anyone who can't maintain their integrity and resist the temptation of swift fortunes will soon find themselves on the path swift misfortune.