Here is what each type of Eevee's move tutor moves covers:
Grass, Ice, Bug, + Steel
Fire, Ground, + Rock
Water + Flying
Water, Ground + Rock
Grass, Ground, Flying, + Dragon
Fighting + Poison
Psychic + Ghost
Fighting, Dragon, + Dark
Now, Fire and Ice both cover the most with 4 each. Water, Grass, and Fairy cover 3 each.
So here is what they'll cover:
Fire, Grass2, Ice, Fighting, Ground2, Flying, Bug, Rock, Dragon2, Dark, Steel
Water, Grass2, Ice, Fighting, Ground2, Flying, Bug, Rock, Dragon2, Dark, Steel
In short, both movesets cover 11 types out of 18 in total.