I've tried using Ice Form shout level 2 (Slen) but I didn't notice any difference compared to level 1 (Iiz). Same goes for throw voice - it however has a lower cooldown, but I couldn't notice anything else. Can someone please explain? Why would I want to be spending Dragon Souls on shouts level 2 and 3?
Higher level shouts usually add more damage, longer effect durations, or more effects at the cost of higher cooldown. (more info here)
For ice form specifically, it increases the amount of time spent frozen and increases the recharge time.
Effects Recharge Iiz Paralysis and 2 damage/s for 15 s 60 Slen Paralysis and 2 damage/s for 30 s 90 Nus Paralysis and 2 damage/s for 60 s 120
Each shout is different. Some are absolutely awesome at level 3 and lack luster at level 1. Look at Soul Tear for example.
Effects Recharge Rii Slight push 5 Vaaz Slight push 5 Zol Soul Trap for 2 secs on enemy, drain health 300 pts and reanimate body upon death for 1 minute.
They higher the level of the shout means the more damage it does with a longer cooldown , for instance when you first learn ' Fus ' of the 'fus-ro-dah' it is weak but once all levels / words are unlocked of it you've gone from tickling bandits to throwing goats off a mountain , hope this helps but Words/levels = upgrades to the shout! :)
Level 2 and 3 shouts become stronger or better in one way or another, depending on the the specific shout. You can read how different shouts get upgraded with levels at UESP wiki. For exmaple, Ice Form paralyzes and applies a DOT effect on the target for 15 seconds at the 1st level, for 30 seconds at the 2nd level, and 60 seconds at the 3rd level; while Throw Voice simply reduces the cooldown with extra levels.