Sid Meier's Pirates!
For indeed the best manual (just a joy to read like almost all Micropose manuals) and relatively easy to catch up, fun sea battles, best worldmap with best map traveling (wind directions)
Blood & Gold
For best melee/firearms combat on land, unfortunately no first person travel on map
PotC with New Horizons mod
Best overall experience, best customization, has rpg elements, quests, good ship combat and customization, sail the Caribbean completely in first person (very relaxing experience for me), traveling on map has unfortunately no wind directions, your own logbook, partly still feels unfinished/unbalanced
Age of Pirates CoAS
Better graphics and a bit better melee combat than PotC, no first person sailing between islands, not as modded as PotC, more cartoon like graphics for characters (but not much). Overall good but I still prefer New Horizons instead.
Sea Dogs Teho
By far the best melee combat from the whole Sea Dogs series. Weapons feel really different in style and handling. It has the best graphics of the Sea Dogs series (but overall still lackluster compared to todays standards). It has a huge amount of content (especially quests) and a pretty good pirates story that feels like the classic novel ones but still fresh (but the translation is sub optimal). It has the best graphics from the Sea Dogs series, too.
The bad: only a fixed starting character (with 3 specializations to choose), can be atrociously grindy and frustrating (sometimes korean mmo-like levelscaling), horrible timed quests where you need a guide in which order and when and how you should take them (lots of dead ends or breaking the game otherwise).
Atm it's sometimes really enjoyable and sometimes just outright frustrating (the no fun kind of frustration where you have to game/exploit the systems instead of playing the game). If the game gets opened for modding and the modding community takes it up it will be the best Pirates game out there so far, by far. Oh btw. I even liked the tutorial. Feels like you earned your ship.
If I had to choose one it would still be New Horizons but the graphics are getting really old by now and melee combat is just boring. I dream of New Horizons for Sea Dogs Teho.