The tax treatment can be quite different between the two choices.
ISOs: The price is fixed based on the grant date. When you exercise, the difference between the value on that date and the strike price is not immediately taxable (per the regular tax rules), but is taxable under the AMT. Exercise well in advance of a liquidity event and you probably won't see much in the way of immediate income even under the AMT. Then when you are able to eventually sell, you pay capital gains taxes on the income. This is another reason why exercising in advance of the IPO can be useful: hold the shares for a year after the exercise and you get taxed at long-term capital gains rates instead of regular income rates. Of course, exercising early has plenty of risks as well: there's no way to know when or if you'll be able to sell your shares. Don't sink too much of your money into them.
Stock grants, on the other hand, are generally taxed as regular income at their full market value when they vest. The 83(b) election protostache mentioned is worth considering when the shares have such a low value right now. You pay tax right away on the current value, which turns out great if you stick around for the shares to vest and they become worth something someday. If you switch jobs or the company goes under, I don't think you get a refund on the tax you pre-paid.