How I think the two classes 'feel' to play (personal opinion):
Protection Paladin
Simpler/easier rotation (arguably).
Feels powerful, solid.
Even in crap gear.
Combo building resource system (holy power).
In direct control of own health and self healing.
Lots of defensive cooldowns and panic buttons.
Lots of self healing.
Great AoE.
Lots of ranged attacks.
You 'feel in control' a lot of the time because you have such direct influence on your own HP.
Your shield 'slam' is also your active mitigation - simplifying things.
Throwing your shield is always fun.
Lots of yellow flashes on your screen.
Look like a Power Ranger in most Tier sets.
Protection Warrior
More involving prio/rotation.
Technical.
Lots of action bar buttons.
Often have a lot of macros to make things work as you want.
Rage resource system a bit of an art to use effectively.
Active mitigation system rage/block/barrier a bit more complex and requires thought.
Lots of defensive options and tricks.
Nice raid utility.
AoE not great without talents.
Feels weak in crap gear.
Feel able to defend yourself well but feel reliant on healers to get your HP up.
Very mobile, lots of running around.
Charging into battle never gets old.
Look like a baddass in most Tier sets.
As I said - just my opinion.