In Dragon War, Dragons retain their classic resistances with a few exceptions such as Alduin, Durnehviir, Skeletal and Vulthuryol.

Fire Dragons - 100% Fire Resistance
Frost Dragons - 100% Frost Resistance
Shock Dragons - 100% Shock Resistance
Poison Dragons - 100% Poison Resistance
Sun Dragons - 100% Fire Resistance
Cold Dragons - 100% Frost Resistance

Instead of a classic weaknesses, Dragons instead share a unique, secondary ability made of both new resistances and weaknesses. Dragons have 50% Stagger Resistance, 50% Critical Damage Resistance, and 50% Weakness to Damage Magicka.
Dragons also benefit from flat 300 Armor Rating, 25% Magic Resistance and a bonus to unarmed damage, based on their level.

In addition, Dragons are no longer forced to stay grounded after they lose most of their Health. Instead, they will spend more time on the ground based on how much Health they have. To force them to stay grounded, you must use the Dragonrend Shout.
They can also infect you with a new disease, Rasp, which reduces the effectiveness of your Shouts.*

Random encounters are also changed, and even if the level and new abilities of a Dragon might be scary at first, only their damage will be higher. That can be mitigated with appropriate preparation. I suggest starting Dragon Rising at level 10, and installing Diplomatic Dragons to remove a lot of early-game pressure after killing Mirmulnir.

Lv. 1 - Dragon
Lv. 12 - Fiery, Frost, Storm, Blood
Lv. 20 - Elder, Snow, Mystic, Sting
Lv. 32 - Ancient, Icewing, Revered, Serpentine, Radiance, Glacial
Lv. 40 - Legendary, Frostscale, Supreme, Miasma, Radiance, Glacial

Furthermore, abilities accessible from the Blades have also been changed.

Esbern's Potion (Dragon Infusion) - You permanently take 10% less damage from Dragons.
Dragonslayer's Blessing - For 3 days, you have a 10% chance of dealing critical damage to Dragons. You deal 25% extra critical damage to Dragons.

Dragons no longer drop armors and weapons; instead, they drop a sensible quantity of Bones, Scales, Gold and Gems to alleviate resource management.

Notes

• Dragon Lairs are much harder to clear if Dragon War is used in combination with Locational Encounter Zones and my Arena Add-On.
• A few fixes have been made to Dragon Lairs, to ensure a better experience with them. A fix for the Mount Anthor bug is also included.
• Dragons LODs have been removed. The same treatment was given to bleeding effect. To restore it, I suggest the usage of Just Blood.

*Patchless compatibility with Survival Mode.

Compatibility

Dragon War is not designed to work in combination with other dragon mods, excluding texture mods, which are compatible out of the box. If you want to expand even more dragon variety, use Infinite Dragon Variants. If you want to use GoT Dragons, a patch is available here.

My Other Mods

Delta’s Repository
Forceful Tongue - Shouts Overhaul
Dragonborn - Shouts Perk Tree
True Teacher Durnehviir
Apothecary - An Alchemy Overhaul
Sil Gahrot - Improved Shouts Learning
Thaumaturgy - An Enchanting Overhaul
Arachnomancy - A Spider Scrolls Overhaul
Oblivion - An Atronach Forge Overhaul
Diplomatic Dragons
The Dragon Cult - A Draugr Overhaul
True Teacher Paarthurnax