The comparison between the Aztecs and Poland is easy to make, but not exactly accurate. Judging them solely on social policies, Poland gets additional ones at regular intervals throughout the game, but the Aztecs tend to accrue more early-on, especially if they adopt Honor first-off and go crazy barb hunting, but it tends to taper off later game. This leads to different outcomes, since, as the Aztecs, a lot of your social policy advantages are inevitably going to end up in those early policy trees, while with Poland you'll end up investing across the board, opening Rationalism as soon as it's opened and getting some options with ideologies.
But really, the specifics lend themselves to wildly different strategies. That continuous stream of culture from kills, coupled with the huge food boosts from the Gardens and the super awesomeness of the Jaguars, makes a unique tall aggressive strategy very viable, and early on your capital can easily be the biggest city on the map. They fit into a weird sort of tall Honor strategy, since Honor makes killing units easier (but doesn't make conquest itself easier, which is the biggest thing), which means you can sweep your way through more culture, and easily fill out both it and Tradition. Later on, they lend themselves extremely well to a culture-based Autocracy game, given their unique ability doesn't wear off, and so you'll still want to make good use of that. Throughout the game they really do well with a military-culture hybrid, which, of course, makes perfect sense for the Aztecs.
Poland, on the other hand, doesn't lend itself well to excessive early aggression, because they don't get much to support it. However, the Ducal Stable gets cities lots and lots of delicious gold and production, which makes a wide, sprawling empire far more attractive. There's also the notion of timing to consider - free policies at every era means you're able to dip into a policy tree once it's immediately unlocked. Rushing into Renaissance and getting a guaranteed Rationalism opening is EXTREMELY attractive, especially since it furthers science, which means you get more free policies even sooner. Since the Ducal Stable lends itself so well to a wide empire, going into Order is a very good plan. ...Or you could do entirely different things. You do unlock Commerce and Exploration as soon as they're opened, so plunging into those means you could make lotsa the moneys and run a huge coastal trading empire. Or you can go Aesthetics instantly and pump up the culture. Or head into Patronage. Poland is a very jack of all trades civ, leaning towards doing well with a wide empire. But they don't do as well so very focused on making an elite culture squad military.
So yes, what you really want to do with the Aztecs is build up a core of super high-promoted Jaguars and stuff, and just, cleanse the world of its military. Be the king of barbarians by wiping them out as much as you can, and pillaging and killing passing units all for yourself. You don't have to conquer cities, in fact, I'd reccomend against that. More enemy cities means more units they can pump out which means more culture. And continue to do this all game. Fill out Honor, make your units awesome, fill out Tradition and Patronage, pump up your cities to being huge with all that culture you're amassing, go Autocracy, make your units even MORE awesome (going with the Legacy and just storming through the resident big militaristic empire is a great idea to amass loads of culture in one fell swoop), and just absolutely dominate with raw culture. You don't HAVE to win a culture victory, you can easily just get in the way of other people winning one and aim for whatever you want.
