"Double rate" doesn't take into account the value of the points. You can get a lot of Chilean pesos for a Euro, but that doesn't mean much. You have to look at exchange rates to know if a given offer is a good deal.

HHonors points are worth, to a very rough approximation, about a third of an AA mile. (SPG points are worth, again roughly, one AA mile each. Look at how many Hilton points it takes to get a hotel award stay, versus how many SPG points it would take to get a comparable award stay. A free weekend night at a low-end Starwood property costs 2,000 Starpoints. You won't find anything in HHonors for less than several times that figure.) So, getting twice as many HH points as you had AA miles to start with isn't a deal after all.

There's no such thing as a universal value of a point. When countries revalue inflated currencies by dropping zeroes, it changes conversion rates to other currencies and may have a psychological impact, but fundamentally it doesn't change a thing. It's the same here. A tall person is tall whether measured in inches or cm, but the numbers are different. Saying that a 72" man is 183 cm tall doesn't make him 2.5 times his previous height. Turning 10,000 AA miles into 20,000 HHonors points doesn't double their value, either.

ETA another data point: When Hilton runs a sweepstakes offering HHonors points as prizes, it values them at 1¢ each for tax purposes. When AA runs one, it values AA miles, IIRC, at 2.5¢ each - that may be a bit off, but it's over 2¢. That's not exactly the 3:1 ratio I generally use, but it's close enough to support the idea of losing value in the conversion despite ending up with twice as many HHonors points as you had AA miles to begin with. (If you give me USD100 and I give you 200 Mexican pesos, you do not come out ahead.)