Actually your taxable income in the second case is less because you made less money. :)

How can you make less money by exercising the same options, but at a different time?

The answer is that they're not the same options. Your respondents are assuming the strike price is FMV at the time the options are issued, which will be different at different times. There may be good reason for that assumption, if it's somehow prohibited to later issue options based on an earlier FMV, but it should have been called out because it's changing more things than just what you'd intended to ask about.

when you declare your income you subtract your cost basis from the sale price. In 1 you paid $10 and sold for $100 = $90 profit you have to pay taxes on. In 2 you paid $35 and sold for $100 = $65 profit. It isn't the time at which you exercise that makes the difference, it is the higher strike price.

EDIT: to be clear, 1 and 2 refer to the original differences in the first post. If we are comparing different exercise time with the same strike price, then the taxes are nominally the same (Because the income tax % you pay depends on your income, you might be able to save money by exercising in a year when your income is low).