Really, it doesn't matter.
You may run into people who tell you in an excited voice, "USFSA is the better program because that's the one that trains Olympians." Well, that's a slightly odd statement. USFSA is the national skating assosciation that interfaces with the International Skating Union, so yes USFSA oversees US elite figure skating for international and olympic competitions. ISI is an association of rinks and stresses recreational skating. You (and your child, if you take your child to learn to skate) aren't elite skaters; Don't worry about which program you're learning to skate in. In fact, I've been told that for many years USFSA did not have a learn to skate program. Instead, everyone learned to skate via the ISI program. Kids switched to USFSA when they had an axel. World champions have come out of both learn to skate programs.
Which rink should you pick? With one exception, I wouldn't make a decision based on the rink's skating program. There's more important priorities: Driving distance, schedule of classes, the rink culture, the quality of the ice, the parking, the presence of people you know, the size of the adult program, even the area of the city. If you take a couple of sessions and don't like that rink, you can switch to a completely different program at another rink. You're not locked into one program. You'll learn the close to the same skills in both programs, but arranged in a slightly different way, since the programs don't line up exactly.
I've known coaches I respected a lot who swore by the learn to skate program for ISI. You can tell you're in this program if they talk about pre-Alpha, Alpha, Beta, Delta and Gamma levels. ISI focuses on recreational skating. There's lots of competitions with imaginative programs: interpretive, props, family, similar pairs, etc. that won't look like USFSA competitions you've seen on TV. It's a really recreational skater friendly program, and focused on making skating fun for the entire family. I started skating in an ISI rink and I like the program.
USFSA Basic Skills for kids levels are numbered 1-8, but there is an Adult basic skills program numbered Adults 1-4. I will say that if you have a choice between a rink that teaches an Adult 1-4 class, or teaches Adults in the 1-8 curriculum, I personally would prefer to take group lessons at the rink that teaches adults using the Basic 1-8 curriculum or go to an ISI rink. I don't understand the logic of giving adults a truncated skating curriculum a la' Adult Basic 1-4, but it seems to be normally what you'll find at USFSA rinks if there's an adult program. I have not found anyone who defends the USFSA Adults 1-4 program. If you understand the rationale for Adults 1-4, I'd like to hear it.
If you get to a rink and find out that they don't have adult classes, ask if you can just skate in the kids classes. My skating guru, the Big Guy, started figure skating in his 30's in the kids curriculum at an ISI rink. A decade later, the kids (now in their teens or twenties) would come up and chat with him on public. No one seemed to care there was an adult in the kids class. I've heard of other adult skaters doing this too.
Regardless of which program you go with, depending on your age, athleticism, and ability you may find you need to repeat certain levels. Don't worry about it. (I met a woman who took Alpha 3 times while she took her grand-daughter to her learn to skate classes.) Have a good time. Better to learn your skills well than to speed through. Learn to skate isn't a race. If you have a significant other, I've seen some married couples having a wonderful time at the rink and sharing the experience of a Learn to Skate Class.
The Xanboni website, talks a lot more about learn to skate as Xan is a dedicated Basic Skills Coach. It's worth it to go through her posts and get some insight into learning to skate programs from a coach's perspective. Her post is much more technical than this one and compares the programs level by level.
There are still some rinks out there that have their own internal learn to skate programs. They may be seasonal rinks, or just have a a long history of independence. Don't worry if you run into this; You're going to learn stroking, crossovers, three turns, and backwards skating, no matter what learn to skate program you're in.
Finally, none of the adult programs I've skated in have had any of the interpersonal drama that seems to come from the parents of kid skaters. I took learn to skate at 3 different rinks (two ISI, one USFSA). Uniformly, the adults were easy going, genial and collaborative.