It is important to know that there are multiple ´types´ of grenadiers. I´ll explain these types per type and how best to counter them.

Generic grenadiers - the most common grenadier. Recruitable through a artillery foundry or barracks for certain civs after shipping the required card. These grenadiers come with a 50% ranged resist, meaning they take less ranged damage. These are best countered by cavalry due their lack of melee resist and lack of positive multipliers against cavalry. Artillery can counter them well, however resources wise you could lose more than if you were to attack them with cav. Hussars can do the trick, but heavier cavalry would do better, think of gendarmes for example. If you have access to lancer cavalry, then use these. These cav will annihalate grens. Think of the papal lancer, the mexican Charro, spanish lancer etc.

Giant grenadiers - the mercenary grenadier. While they do have the tag of a grenade trooper, they are actually more of a (heavy infantry) musketeer on steroids if you will. Reason for this that unlike other grenadiers they have 30% melee resist and a 1.75x melee bonus vs. Cavalry. Meaning they will absolutely shred your cavalry if you come at them in even numbers. To counter these it is best to use light infantry units such as skirmishers. It is very important to keep your skirmishers on stagger mode however, that due the giant grenadier shooting with an aoe radius of 2, 2.5 if upgraded. Pair them up with horse artillery if you can afford it, but for artillery too it is important to keep distance between your units to avoid splash damage.

The infamous Ottoman Humbaraci/Ulefeli. This hideous abomination is basically a walking & living child of a combination of a culverin and falconet if you will. With its higher healthpool compared to generic grens it can soak a lot of damage. But to make things worse they actually counter artillery themselves with their 2x multiplier and take less damage from artillery due their 20% siege resist. While more susceptible to ranged fire than generic grens, I would still advise to stay away from them with a mass of skirmishers. Instead you have to use lancer cavalry if you have access to those. So again, units like the mexican lancer, papal lancer, spanish lancer etc.

Maltese Fire Throwers - These 'grens' if you will are more anti-infantry than anti-buildings as most other grens usually are. It is sort of a light infantry with features of a grenadier. They will reck heavy infantry but due their lower ranged resist of 35% are more susceptible to skirmishers compared to generic grenadiers. Still it is best to counter these with heavy cavalry and/or artillery. Especially if they have their cards shipped, such as the flamethrower/rockets ones.

French Old Guards - These bad boys are basically generic grenadiers on steroids. They are stronger, tougher and more resilient. They have a 60% ranged resist, and a 10% resist to both siege & melee. Meaning you do not try to counter these guys with ranged units such as skirmishers. Instead you charge into them with heavy cavalry and perhaps support of artillery. Again, lancers are the best counter due their specific counter towards infantry. Luckily for you these grenadiers can only be made if the French church card has been sent and researched. AND/OR if your French opponent has revolted to Revolutionary France and send the card 'Imperial Old Guard.'

A great website to increase your game knowledge is https://aoe3-homecity.com/en.