Hilton gives one the option to earn points and points; fixed or variable miles with airline partners. How can I decide which one is better for me? I have Delta as airline provider.
A lot of this depends on how you value your points.
First of all, fixed miles is a bad deal unless your stays are all of only one night at Hampton/Homewood (and even then, unless you have a rate below 100 dollars all the time, it's a questionable choice), or ~2-3 nights at other properties (total dollar value of stay <500). Variable miles gives you 1 mile/dollar spent, whereas fixed is a rate of 100/500 per stay depending on the property type.
At this point, you need to figure out the relative value of 5 HHonors points versus 1 Delta SkyMile.
People value points differently, depending on their travel preferences. The best way to do things is to price out a few different hypothetical trips you might want to use your miles for, whether that be a flight to see family for Thanksgiving, or that dream vacation to Bangkok. Figure out the cost in points for each, and compare it to the cost in dollars to come up with a value per/point.
The internet consensus, for the most part, seems to be that Delta miles are worth somewhere in the range of 1-3 cents per mile. HHonors points, by contrast, are considered to be worth around half a cent. However, as I mentioned, your own travel patterns will effect this heavily. If you mainly want to use the rewards to fly to visit family, you probably won't need a hotel - your valuation of miles is probably a bit higher. If you're fond of taking road trips, and eschewing airports, maybe hotel nights are of more use - especially when you can use them at some low-demand locations with really favorable rewards rates along an interstate in the middle of nowhere.
Do the math and decide for yourself.