While I havent played Pirates, so I have no knowledge of which is better at what aspects, I would encourage you to stick at Port Royale (especially the first one) for a bit longer. It definatly plays a little slowly at early on, but it ramps continuously up as the game progresses and you can have an aweful lot going on later in the game.

It also lets you play how you prefer. You can have a fleet of pirate and merchant killing ships, selling you ill-begotten goods and ships; or alternatively, as you seemingly desire, you can focus on establishing an economic empire of multiple companies, numerous rent earning houses, and automated trade routes setup to keep all the goods moving to the required locations. You can balance it out to your preferred playstyle and then mix it up with some missions and map/riddle solving.

(Note of caution: don't expect empire building to come easily. In my experience it is significantly more time consuming than going the large ship killing fleet route, but it can be very rewarding to set up a highly profitable automated trade route if you put the effort in)

Finally, if you are looking to speed up some of the boring bits, such as waiting for your ship to traverse half the map on a long voyage, I would recommend utilizing the speed controls. '+' and '-' increase and decrease speed. However you then do loose part of the immesrion of just how vast the map feels when you leave it on standard speed.

Port Royale difinatly has a strong economic focus that you seem to be looking for. It just takes a bit to learn and get a handle on it. So I hope this helps or encourages you to give it another go.

(edit: Im more relating my experiences to port Royale 1 here as I really prefer it to the 2nd. ie, original looks nicer, prefer the UI, has multiplayer etc etc... )