(what is commonly said about each other & the real difference).

ITF assessment of  WTF stylists:

All they do is fancy foot and legwork with a lot of sound. No real power. Everything is geared to competition and tournaments. No spiritual arts, and a lot of good foot techniques such as twisting front kick(a kick that springs up from a standing position both feet facing forward, foot is twisted inwards and kicked up towards the opponents nosebridge at an angle)are lost, and everything is competition oriented. The practicality of the martial arts is lost for speed and points in tournaments. Upper body and hand movements are not emphasized nor does it call for hitting/striking the face/head as in real fighting, or close range when someone is tackled.  Thus the students are only skilled in playing  tag points . No real practical value in actual fighting. The head of WTF is not a TKD practitioner but a bureaucratic figurehead which is why WTF certificates are signed Dr. Un Young Kim. He has neither demonstrated nor taught TKD.   The WTF patterns are of no aesthetic value, it is just a breakdown mix and match of ITF forms. No beauty in forms. Taekwondo?  Gaekwondo  is more like it.(Note:   Gae  is dog in Korean, loosely translated, it means  dog pawing ).

WTF assessment of ITF stylists:
Outdated and limited kicking techniques taught by old masters that have no practical application & imagination for WTF sparring. Non contact or light contact  pussy footers -because one is conditioned to fight non-contact or light contact,  they get blown away in  real  hard full contact sparring situations. Impractical sparring moves-eg. blocking instead of dodging. Moves are too slow for practicality and vulnerable. (e.g. plain wheel kick, where the heel is turned in an arc towards the opponent s head by turning back without hooking at the knee ).  Too low and wide stances that slows down each movement and telegraphs your move. No power nor speed in moves. No efficient aerial kick techniques that require high skill which can be devastating,. No innovations or development in their moves. Thus the students have limited skills.  ITF TKD? Gimme a break.

Rules of WTF(simplified terms).
WTF sparring is tournament oriented.

1. Hits must be on the certain target areas above the waist line for points.
2. No punches allowed to the face. If punch is done to the body, one must hit to the body with a  forcible impact to the opponent.
3. Kicks to the head allowed.
4. No grabbing or holding the opponent.
5. No points for hitting in the back.
6. No sweeps or take downs. 
7. Protective gear (including forearm, shin, head, chest, and groin protection )and now doboks must be sanctioned by WTF

Rules of ITF(simple terms).
ITF is traditional training oriented. Tournament Rules
(Again, this is general and varies in each splintered ITF-style group).

1. Protective gear required(the level of protection depends on the instructor).
2. Light padding on shins, knees, foot, and arms.
3. Light head gear.
4. Timed sparring.
5. Points for certain targets including hand techniques. Stopped for points(in some).
6. Non, light, or medium contact. (Full contact is rare, but is allowed in some tournaments). 
7. Chest protector(depends on instructor).

The real difference between ITF and WTF
ITF being traditional adheres to an  equal emphasis  on patterns, breaking, sparring, & self-defense techniques. WTF has  more emphasis  on sparring aspect than patterns and self-defense. That is not to say WTF does not have patterns or self-defense. Breaking in WTF however, is not much emphasized as breaking in ITF.

Which is better?  In my opinion, the objectives of ITF and WTF are different. ITF(traditional martial art TKD) and WTF(tournament geared TKD) are two different systems that has diverged from the same origin.  The best answer would be the better TKD stylist. The question is more like who is the better player? Comparing the better squash player vs. the better racquet ball player IMHO does not do justify who is better, even though the  game may be similar.
by W.Rhee