The figures I always heard were that FAI (and surrounds) have a 50% chance of seeing the aurora on any given cloudless day, whereas ANC has about a 20% chance of seeing the aurora on any given cloudless day. The key words are
on any given cloudless day. (The 75% figure might be accurate overall, but if 1 out of 4 nights is cloudy, that would explain the discrepancy between our figures.)
ANC being a maritime climate and, on average, quite cloudy (and significantly more cloudy than FAI), that means that for any given length of stay, the chances of seeing aurora in ANC are quite small. In fact, in the 17 years I lived there, I could count on a couple of hands the number of times I saw the northern lights. (Part of that, too, was that even when they were reportedly out and the weather was clear, they'd often be so faint that the light pollution of the city would overwhelm them, and I eventually gave up the 2am drives to Arctic Valley or wherever to try to catch the faint whisps of green they invariably ended up being.)
While far from immune to cloud cover, Fairbanks is 300 miles from the nearest ocean and bounded by major mountain ranges to the north and south (the Brooks Range and the Alaska Range) and hills of several thousand feet to the east and west, which tends to keep things much drier there. (Fairbanks proper sits in a bowl on the edge of the Tanana River Valley and sometimes suffers from wintertime temperature inversions, but a short drive into the hills around the city addresses that.)
So given the higher percentage of clear nights in Fairbanks along with the better positioning nearly directly under the auroral oval (in other words, the aurora doesn't need to be as "strong" to be visible), Fairbanks is obviously a much better place to position yourself for aurora viewing than Anchorage. It's also better than just about anywhere else you can go and definitely better than anywhere you could fly on AS--OME and OTZ have more cloud cover than FAI (being directly on the Bering Sea) and BRW is actually too far
north to be directly under the auroral oval (and also suffers from long periods of cloudy days). Somewhere like Fort Yukon might be
slightly better positioned than FAI, but it's expensive to get to and lacks tourist infrastructure.
That said, weather patterns in Alaska tend to be long-ranging. We generally don't have battles between warm and cold fronts that cause convective activity and explosive thunderstorms that are swept away in a few hours. Instead, weather in Alaska comes from large low-pressure systems that slowly come from Siberia and move over the state (usually in a southeasterly direction). That means that while
on average only 1 out of 4 nights might be cloudy, that 25% is often clustered together in a span of several days in a row. Then a high-pressure ridge comes along and clears away the clouds and it'll be clear for a while. If you only come to the state for a few days, the chance is not insignificant that you might run into one of those stretches of cloudy days, and relief might be several days away.
On average, the late winter is the clearest time of the aurora-viewing season. I would say February into March is probably just about the most ideal time of year to go. Just beware of the cold--here's the climate data for FAI from Wikipedia:
The cold
will soak through whatever the best jacket you think you have is.
On the upside, FAI has relatively little wind (indeed, Fairbanksans complain that ANC feels colder in winter because of the breeze).
Also on the upside, rental cars tend to be cheap in Alaska in the winter because no one else in their right mind is there.