Both of them are great in their own ways. Let's take a look:
This guy has great Defense (base 131) and almost as great Special Defense (base 116). While it's a great lead and a good Spikes/Stealth Rock user, it has a major weakness to Fire, one of the very common types used in competitive play. Mega Charizard Y + Drought + Flamethrower = Death to Ferrothorn.
But even with Ferrothorn's big weakness, it has a bunch of resistances to make up for it. It resists 10 types, and 6 types only do neutral damage.
Due to its Grass Typing, moves such as Spore or Stun Spore will not effect it. This can be useful for those who use Pokemon such as Breloom + Spore or Venomoth + Sleep Powder/Stun Spore.
As for movesets, most Ferrothorn I see have this:
Ability: Iron Barbs
EVs: 252 Special Defense, 200 Defense, 58 Attack
Seed Bomb/Power Whip
I myself haven't used this Pokemon, though it looks like a pretty great physical wall. It has monstrous Defense (base 184) and great Attack (base 117). However, unlike Ferrothorn, it doesn't have the Special Defense (a measly base 46) to really take a special attacking move (unless it wasn't very effective). However, the great thing about Avalugg is that it has access to Mirror Coat through breeding, as Dragonsmasher stated.
Another downfall is that Avalugg is just a plain Ice type. It is weak to so many more moves, and only resists one type, which is Ice, its own typing. Almost any special move could take this guy out. However, it has access to Sturdy, which is its hidden/Friend Safari ability. With Sturdy, it would be able to tank a Flamethrower or an Aura Sphere, and use Mirror Coat to wreck major havoc on the opponent's team.
Here is a recommended moveset for this giant ice... alligator... monster thing.
Ability: Sturdy/Ice Body
EVs: 252 Special Defense, 100 HP, 100 Attack 58 Defense
In conclusion, though both Pokemon are great, I think Ferrothorn would be a better choice. However, we are all subject to our own opinions as to who we think is better, right? Go with your gut, or try raising both for different teams!