Take a look at this website: http://www.natkd.com/tkd_forms.htm
You will see a table the lists the forms for the ITF, and also the WTF.
The WTF forms are the "Palgwe" and the "Taeguk" forms listed. If you watch some of these, you will notice that the Palgwe forms look more similar to the ITF forms you know.
The WTF style is constantly changing and evolving and is the style recognized by the South Korean government and the IOC (International Olympic Committee.
WTF is an Olympic sport, but there is a common misconception that WTF schools only teach sport, or that they do not include self defense. While sport is a major part of WTF TKD, you have to realize that it was also a combat art and is still currently taught and used by the South Korean military and secret police.
An example of a kicking difference is the WTF evolution of the rear leg round kick, versus traditional rear leg round kick found in ITF TKD.
In ITF, the chamber position is paralell to the floor, turning the hip over and delivering maximum power from the hip.
In the modern WTF version, the chamber position perpindicular to the floor (the same chamber as a front kick) and the hip is only partially turned at the last second.
The idea behind this is that you are eliminating movement and adding a slight deception in the delivery of the kick.
Opponents say that this results in less power because you don't use all of your hip, but advocates say that the increase in speed more than makes up for that because mass (your foot), times acceleration (your speed) = force (your power).
I have done both, but I've only done WTF the last 2 years. My personal opinion is that the WTF kick is significantly faster and is not lacking in power. It does not look as good on video, it's not as pretty, but it is more effective in sparring.
There are also differences in the sparring and rules. The WTF is 100% full contact, no points are awarded for light contact (with the exception of local tournaments with kids and stuff). There is also no break after each point. There are 3, two-minute rounds of continuous action. Judges score the bout and you can see the score on a monitor as the match progresses. There are no hand techniques to the head, and no kicking techniques below the waist. Scoring to the body is worth 1 point, kicks to the head are worth two points. Also, wearing a hogu (chest protector), shin and forearm guards, and head gear is mandatory. Fist and foot protection is optional.
In contrast (unless it has changed), ITF sparring does allow hand techniques to the head, but not at full contact. Foot and fist protection is mandatory, but other safety equipment is optional. Matches are scored on a point by point basis, meaning a restart after each clean point (like in the movie karate kid).
There are also a few historical arguments between the two factions. There are also now 3 different ITF organizations each claiming to be one that goes back to General Choi.
My feeling is that they are both good styles. ITF is definitely more traditional and has a heavier influence from the Japanese/Okinawan styles of karate. WTF is using scientific methods to further develop and modify techniques. Both have big internal politics to deal with too.
According to TKD Times magazine, a merger between the WTF and ITF will happen in the next few years. TKD, as a style, has been taking a beating from other styles and people trying to discredit it as a legitimate form of self defense or fighting. I think a unification would help strengthen the style and help fight back against this bad publicity.
Good luck.
James