Having played in both, (APA - where I ran a league for upwards of 8 years and played in said league for 10+) and (NAPA - where I've played for over a year and a half now), I've been to the APA Nationals 4 times, and their singles twice. I've now been to the NAPA Nationals once (in my first year of playing). I'll give my opinion for what it's worth.
First, APA puts the players a very distant second to their own business interests. They have for years tailored their league so that handicaps inevitably rise over time while keeping a strict limit on team numbers such that teams must split and reform. This isn't the worst thing in the world but it does create problems if you're looking for a league to play in with friends. Over time it becomes impossible. NAPA isn't nearly as strict, giving LO's flexibility to configure leagues to avoid this on the local level. APA simply wants you to go up to a point where you have to split, create more teams and then expand the league. It's always business first, player second.
Second, APA is tailored for the less skilled players in their normal leagues. Everything about their scoring structure gives an advantage to the lesser skilled players from the double reduction the more skilled players suffer from, to the new 3 point scoring system which favors lesser players getting valuable points in many cases where they haven't even earned them and it's because of a single mistake by the higher skilled player giving them a single game which might put that lesser player on the hill, which in turn comes with valuable points. (This same system took away so much strategy from the team concept as well.) All of these same things lead to the lesser players going up sooner than they might otherwise, which leads to issue number one above at some point. NAPA has none of these hangups. The race matrix isn't stacked one way or the other for lesser or higher skilled players. It's steady and even from top to bottom. As for bonus points, there's no double reduction putting players on the hill for winning a single game whether it was given to them or won by themselves.
Third, as previously mentioned, scoring is so much simpler in NAPA and now it's even better with it being paperless as well.
Fourth, sandbagging. This is a big one. It's ingrained in APA. They don't want to admit it, but it's there, in nearly every league. It was in my home state, it is in the local leagues where I live now. It's part of the system and it's there because of the system. There are too many holes in the handicap system. I know the system because of my past history with running a league. I won't divulge here, it's not my place, nor would I want to do that to the APA for any reason. I can tell you though, that the handicap system is flawed from a player's perspective. It is geared to issue number one and because of that, it has holes that can be exploited by sandbagging. On top of that, they don't strictly enforce their own rules against because most LO's don't want to have to kick players from their leagues and lose revenue (back to the business thing). NAPA has ZERO sandbagging. You win, you eventually go up. You lose, you eventually go down. There's no sandbagging and winning, period.
Final comments....
APA still rules the roost because they've been there so long. They have one big thing going for them. That lure of Las Vegas for the Nationals. Most don't realize that they could take the money spend on playing in APA all year and have their own expenses paid trip to Vegas and have quite a good time. I believe that if NAPA would move their Nationals to Vegas it wouldn't be long before APA might not be on top of the heap anymore. NAPA has a better scoring system, better flexibility. More transparency in seeing what a player has done on their website without hiding everything behind passwords, etc.
There are many other things, such as annual memberships for APA (none for NAPA), money paid out each session depending on how you and your LO want to structure your local leagues. It's far easier to qualify for the NAPA Nationals than it is the APA. The Nationals are run smoother, certainly for things like side tourneys at the events. You can also qualify in multiple events at the NAPA Nationals where you won't have to worry about losing to a sandbagging team that doesn't get DQ'd til the end of the tourney when it's too late for you to continue on. I see very little that APA has over NAPA right now if you look past the Las Vegas thing and if you're serious about playing that's easy to do.
Just my thoughts on the leagues and why I play in NAPA leagues right now.