Age of Pirates: Caribbean Tales compares to Sid Meier's Pirates!, this is your review...
If you're a fan of the Patrick O'Brian books, or the Hornblower TV series, or just generally a Naval Combat buff, then Age of Pirates' simulation will reward you to the point that the waiting game before engagements is actually satisfying... all that's missing is a junior officer to keep watch for enemy maneuvers while you're in the kitchen grabbing some coffee.
Ship damage works well, although you have to aim manually to see some of the more satisfying results; such as when you fire chain shot at an enemy mast and see it topple.
The one thing that it fails at in sea combat is surrendering. The enemy won't strike his colours unless you ask him to, and if he accepts then your entire combat squadron (you can make some of your ships into cargo ships and order them away from fights) is teleported to the surrendering ship. It really jarrs the battles, however there are a decent set of options for communicating with hostile and friendly ships. When you see that you can ask a passing ship for the latest news, you realise that Akella have gone a long way towards authenticity.
But just like Sid Meier's Pirates, the authenticity is selective. Akella's take on the pirate life is a lot more mature than Meier's. There's no romancing the governor's daughter, but there is a fair bit of politics involved. All of the officers have different loyalties and the nations have different policies. You can't make any act of aggression without angering someone, and although that's part of the fun it's also a costly mistake in the early game where trading is more lucrative than missions.
Officers are a key part of the game. You hire them in taverns, and at the start they're expensive but valuable. The officers on your crew boost your character's stats; for example if you hire an officer with better gunnery skills than you and assign him as your gunner, then his skill will be used in all gunnery operations. Much, much later in the game your character will be so skillful that you won't need as many officers on your ship, but you'll have them captaining other ships in your fleet and running colonies for you. It's at that point that you'll wish you had groomed your officers to be captains and governors instead of upgrading whatever skills you'd hired them for, as finding good captains and leaders is a mission all on its own.
Ground combat is very different from Meier's version. It's hard to decide which is better. While Pirates! gives you the rock-paper-scissors game, Age of Pirates is more traditional with a selection of attacks varying in speed and power, and parries and blocks that vary in risk/reward for counterattacks. This is a good thing, because the combat is so clunky that your general strategy will serve you much better than your reactions. Combat is generally in two stages, where you lead your crew against the enemy ship's crew in a manic battle and then proceed into the Captain's Cabin for a one-on-one. Generally the crew vs crew combat is decided by strength of numbers but in a close call you have to apply your character to the battle decisively.
All in all, deciding between Sid Meier's Pirates! and Age of Pirates comes down to what you like best about the pirate genre in general. Age of Pirates goes for a more epic take while Sid's is more fantasy fun, and that shows in the length of the games. With Pirates!, you character grows older and has to think about his retirement. It cuts you off and makes you end the game on a high before setting out to beat that high in a new game. If you didn't like that aspect, then Age of Pirates will make you think twice, because it takes ages. The number of battles as you progress your character from petty thief to trader to merchant to pirate to pirate king to founder of a new nation and conqueror of the Caribbean... if you're playing on simulation mode, then two or three battles is enough for one gaming session and that just about covers a trip between two colonies.
So it really is all about what you want from your pirates game.
One word of warning for those looking forward to Age of Pirates' sailing simulation: the sails are all wrong. They go so far as to billow in the wrong direction in some ship models! Also the ships will never change their sail configuration: your frigate will not hoist staysails, ever. Your crew will not take the square sails down when you're beating to windward. It's hard to forgive such an oversight but the forgiveness will be worth it. It really will.