The Portuguese are a versatile civilization due to them possessing bonuses in many categories.
The key economic bonus available to the Portuguese is that they gain a Covered Wagon every time they advance in age. This allows for rapid expansion across the map and quick training of Settlers in the mid-game. They also start with one extra settler, although this early-game advantage is extremely brief as they have no home-city settler cards.
Their Explorer is fairly unique - he possesses a "Spyglass" feature, allowing him to temporarily view a selected spot, essentially mimicking a static Hot Air Balloon. In addition, the Portuguese can send two additional Explorers with the Bandierantes card, essentially tripling their Explorers' capabilities.
The Portuguese have a fairly strong coastal defense - they have the unique TEAM Coastal Defenses card, allowing Town Centers and Outposts to gain an additional damage multiplier against ships. They also have the best walls, though they can share it with their allies if it is enabled with the TEAM Improved Walls card. They also possess the TEAM Early Dragoons card, allowing them to create Dragoons (and Cavalry Archers/Ruyters for the civilizations who have them) in the Colonial Age, allowing for an early ranged cavalry counter to the dominant Hussars and Cossacks at the Colonial Age.
Along with the Ottomans and Spanish, the Portuguese are able to hire Ronins in the original game - however, they do have an early game advantage as they are the only civilization to be able to hire them in the Fortress Age, a nod to the explorers who visited Japan far earlier compared to the other nations.
They also possess strong Musketeers and Dragoons, who are their Royal Guard units. The Cassador is their version of the Skirmisher, possessing less health, but higher damage and ranged resistance. The Organ Gun is also their version of the Falconet, although they lean more towards more concentrated burst damage.
In other words, the Portuguese army is made up of more specialized units than many other civilizations, but when properly coordinated and micromanaged, they can be extremely difficult to defeat. However, this means that they require a degree of subtlety that makes them ill-suited to inexperienced players.
The Portuguese are often disliked for their difficulty to play, and this is plausible, since there are so many different directions a Portuguese player could go.
Compared to other civilizations, the Portuguese do not have access to early siege units, since the Organ Gun is extremely ineffective at taking out enemy buildings, and thus they must wait until the Industrial Age for Monitors and Mortars. Their army must also be diverse to maintain effectiveness; an army of only Cassadors and Organ Guns will mean an attack will surely fail, as properly upgraded units like Imperial Czapkas can easily destroy them in seconds due to their low health.
They do not have any Settler Cards, so the only way to get more settlers is by training them at Town Centers, which can be problematic with low resources. Although the Covered Wagons can be spread out to avoid being detected, they will be eventually found and destroyed if their economy is still weak. Strategically placed Forts will prove troublesome without Mortars or Monitors to assist in destroying them, as high casualties are expected unless the cannon trick is used - where the attacked unit goes next to the location of the cannons to avoid taking damage from them.
The nature of how the Portuguese are played also means that they must quickly advance in Age, since they demand a diverse army which requires significantly more resources compared to other civilizations. Failure to do so means they will lag significantly behind and be overwhelmed.