There are more differences to each nation than are listed here, so these are only the ones that have the biggest impact on playstyles. Comment if you have anything to add or find anything wrong.

Availability: Vanilla
Type: Rush

+Archers and light infantry that are cheap and train quickly
+Cheap academy farm and artillery upgrades
+Academy builds quickly
~17thc pikemen +1 attack, low armor
-No 18thc upgrade
-No native musketeers or dragoons
-Town centres and barracks support low population
-No balloon to reveal map

Availability: Vanilla
Type: Balanced

+Workers 100% more health (Seems to have changed)
+Very cheap 18thc pandur high damage musketeer
+Roundshiers strong melee infantry, low damage, high defence
+17thc Pikemen, and roundshiers have armor against bullets
+18thc balloon to reveal the map
+Access to fast 17thc croat calvary
~17thc musketeers, slow training, has armour

Availability: Rise to Glory DLC
Type: Late

+18thc Musketeers high damage and long range, but slower training
+Grenadiers first attack upgrade costs 40% less
+18thc balloon to reveal the map
~Stables build 80% faster but are weaker and more expensive
~Dragoon defense upgrades cost less, attack upgrades cost more
-Pikemen upgrades cost more

Availability: Days of Brilliance DLC
Type: Late

+Strong 18thc musketeer, high damage, long range, but more expensive, slower training.
+18thc musketeer can throw grenades (Seems to have changed)
+18thc upgrade costs slightly less
+18thc balloon to reveal the map
~Stables build faster, but cost more
-Some pikemen upgrades cost more

Availability: Vanilla
Type: Balanced/late

+17thc pikemen with armor against bullets
+Strong cuirassier cavalry
+Cheap 18thc highlander musketeer, high damage, high HP, slower training
+18thc musketeer
+18thc balloon to reveal the map
~Fast building stables, need less wood and no stone, but require more gold.
-Expensive upgrade to 18th century

Availability: Vanilla
Type: Balanced

+17thc pikemen with armor against bullets
+Cheap 18thc chassuer musketeer, high damage, long range, slow training.
+18thc musketeer
+18thc balloon to reveal the map
+Access to the King's Musketeer in 17thc stables. Highest shooting damage in the game.
~Lots of small differences to other nations

Availability: Path to Grandeur DLC
Type: Balanced/early

+Unique musketeers (Hadjuks). Fast fire-rate, fast training, low damage, low range
+Unqiue fast cavalry (Hungarian Hussar). Avaliable in 17thc
+18thc barracks builds slightly faster
+18thc musketeer
+18thc Szekely musketeer. High damage, Long range, slow training.
+18thc balloon to reveal the map

Availability: Days of Brilliance DLC
Type: Balanced

+17thc pikemen upgrades cost less
+17thc dutch musketeer, faster fire-rate, faster training
+18thc musketeer
+18thc balloon to reveal the map
+Town halls slightly stronger
~18thc dragoon increased HP, but slower training and damage
~Cuirassier defense upgrade cheaper, attack upgrade expensive

Availability: The Golden Age DLC
Type: Balanced

+Priests cost less, heal faster, but train slightly slower
+17thc musketeer defense defense upgrades cost slightly less
+17thc pikemen defense upgrades cost less
+18thc pikemen upgrades cost less
+Grenadier attack upgrades cost less
+Advance to 18thc costs slightly less
+18thc musketeer
+18thc balloon to reveal the map
+18thc Piedmont dragoon, shorter training, lower HP
~Cuirassiers attack upgrades cost less, defense upgrades cost more

Availability: Vanilla
Type: Balanced/Rush

+Winged hussar strong and fast cavalry, but train slowly
+17thc pikemen cheap and fast training, but no armor
+17thc musketeer cheap anf fast training, but low damage.
+18thc musketeer
+18thc balloon to reveal the map

Availability: Path to Grandeur DLC
Type: Balanced

+Very cheap 18thc volunteer musketeer infantry
+18thc musketeer upgrades cost less
+18thc balloon to reveal the map
+Academy cheaper
+Town halls slightly stronger
~17thc pikemen cheap, train & attack fast, but no armor
~Grenadier attack upgrades cost more, defense upgrades cost less
-18th pikemen upgrades cost more

Availability: Vanilla
Type: Balanced/late

+17thc pikemen with armor against bullets
+18thc Prussian Hussar fast training, lower attack and defence.
+Workers 100% more hitpoints (Seems to have changed)
+18thc balloon to reveal the map
~18thc musketeers very strong, but expensive and slow to train

Availability: Vanilla
Type: Balanced

+17thc spearmen with armor against bullets
+Barracks are cheap and don't cost gold
+Cheap houses only cost wood, slightly stronger
+18thc musketeers
+18thc balloon to reveal the map
~17thc Strelet musketeer slow training, low range, but very spammable.
-No 17thc dragoon
-Town centre and barracks support low population
-Workers build slowly
-Expensive stable and diplomatic centre

Availability: Rise to Glory DLC
Type: Balanced/late

+17thc pikemen attack upgrades cost slightly less
+18thc pikemen upgrades cost less
+18thc musketeers use less iron and coal
+18thc musketeers faster fire-rate
+Strong grenadiers
+18thc balloon to reveal the map
+17thc dragoon upgrades cheaper
+18thc Cavalry Guard heavy cavalry replaces Cuirassiers

Availability: Guardians of the Highlands DLC
Type: Balanced/rush

+New castle building that trains clansmen.
+Clans Bowmen Long range, High damage, High HP
+Clansmen, Very High damage, Very high HP, Long training
~ High damage, shorter training, pikeman but without armour
~ Long range musketeer, longer training.
~17thc balloon that reveals the map, more expensive though.
-No advancement to 18thc

Availability: Vanilla
Type: Balanced

+17thc pikemen with high damage, and high armor against bullets
+17thc musketeers with armour and higher damage, but longer training
+18thc musketeers
+18thc balloon to reveal the map

Availability: Vanilla
Type: Balanced

+17thc pikemen with armor against bullets
+18thc musketeer
+18thc baloon to reveal the map
+17thc slightly faster Swedish Reiter production, less armour
~18thc pikemen 2x gold cost, but +1 attack
~Lots of little differences

Availability: The Golden Age DLC
Type: Balanced/Rush/Late

+17thc pikeman have fast upgrades, high damage. Slightly slower training.
+18thc musketeer
+18thc long range jaeger musketeer, high damage, longest range in game, slow training.
+18thc baloon to reveal the map
~Hussars cost more, but are stronger

-Advance to 18thc costs slightly more
-18thc barracks builds slower

Availability: Vanilla
Type: Rush

+Strong 17thc janissary musketeer, slow production, high damage.
+Fast training melee infantry
+Barracks are cheap and don't cost gold
+Stables are strong and build quickly, but additional ones are more expensive
+Town centres are cheap
+Cheap farm, artillery, and ship speed upgrades
-No 18thc upgrade
-No native dragoons
-Infantry have no armor
-Barracks support low population
-No balloon to reveal map

Availability: Vanilla
Type: Balanced

+Cheap town halls, houses, and barracks
+Cheap 2nd mill upgrade
+Academy builds quickly
+Academy worker build speed, building strength, ship speed upgrades cost less
+Mine +40 upgrade cost less food
+17thc balloon to reveal map, but expensive
+Peasants cannot be captured
+Good serduik 17thc musketeer, High damage and spammable.
-No native melee infantry or dragoons
-No 18thc upgrade
-No stone wall or tower, but has wooden walls
-Barracks support low population

Availability: Vanilla
Type: Balanced

+17thc pikemen with armor against bullets
+18thc musketeer
+18thc balloon to reveal the map
+Slightly cheaper horse speed upgrade.
+Dankest Nation, personally recommend (colourfit)
-Large Town Centre

Thanks to colourfit for keeping the guide updated and tidy. If you found this guide helpful then check out colourfit's awesome Cossacks 3 YouTube channel! https://www.youtube.com/channel/UCAj-ms1m9yuuozkPCGBx0zQ/videos