1. Get options, pay nothing.
2. Exercise options, pay AMT.
3. Sell stock, pay capital gains.
(Please point out anything missing; it's missing because I don't know about it.)
Assume that the timing of step 2 is nondiscretionary and the stock price is temporarily depressed when it occurs.
Assume that you have to pay the AMT by selling some of your stock until you've sold enough to cover the whole AMT.
If the AMT is a lump sum (seems... unlikely?), then the depression in the price at the moment you have to pay it is bad for you.
If the AMT is a percentage of the value of the stock (my guess?), then by the assumption that you have to pay for it by selling stock, you're going to lose a fixed percentage of your stock no matter what the current stock price is.
If we relax that assumption and you take out a loan to pay the AMT, the depression in the stock price is good for you, because you end up making a profit on holding your shares while they recover.
In step 3, you sell your stock at the "natural" price. I guess that since the stock was temporarily depressed, it's now higher and you pay a capital gains tax on the difference. Is the tax rate higher or lower than the rate you paid for the AMT? If it's equal, what difference did the temporary depression of the stock price make?