1. Colonizer is pretty much outright superior to Engineering simply because it makes distance decay from shipyards irrelevant. EVERY colony can start with a shipyard with Colonizer if necessary. Consequently the only reason to choose Engineering is if you chose Colonizer also.
2. Naturally Colonizer is much stronger on larger maps with more planets to colonize. Consequently Colonizer is a trait that scales exponentially to numbers of habitable planets. On smaller maps, it's really not that impressive. On larger maps... whooosh.
3. On systems with multiple worlds, colonizer is ESPECIALLY strong because it allows ONE planet to rush the shipyard, and all of the others can rush factories, granting a +25% production bonus to new starting worlds.
With the preliminaries out of the way, on to the meat of the argument:
The PRIMARY advantage of colonizer is that it allows your new colonies to IMMEDIATELY begin spamming out colony ships. Shipyards are one of the most expensive early buildings in the game and Colonizer effectively removes that block. With free shipyards on your border worlds, this means your border worlds can spam CHEAP CUSTOM DESIGNED COLONY SHIPS (the ones without engines using "small hulls"). This allows you to fill out the worlds near your border, while your core worlds can spam out EXPENSIVE MANY ENGINED COLONY SHIPS to leapfrog FURTHER past your borders. In other words, you don't have to waste desperately needed manufacturing points from your core worlds in the early game on building colony ships for your other non-colonized border worlds. Your border worlds can take of that job.
On the right map, this means you can effectively win the game in the first 50-100 turns because of how badly you've out colonized the AI. The rest would just be cleanup.
Furthermore, not only does grabbing more worlds means more production, it ALSO means more ideology points. THIS IS A HUGE DEAL. Ideology points are one of the hardest things to get after the early game (unless you choose Zealot) and getting as many as you can early on GIVES YOU A HUGE LEG UP. 50 colonies with Benevolence level V Research for example means a minimum free +250 Research every turn. In the early game, this is literally all you need.
Is Colonizer better than the other traits? One smaller maps or on maps with fewer habitable planets: probably not. But on larger maps with more planets and more room to expand IT IS ONE OF THE STRONGEST TRAITS IN THE GAME because it can effectively win you the game before the AI is ready. If you manage to get 120 colonies by the time an average AI gets 30, that's it. No need to play anymore. You've won. That's why it's so powerful.