[Note: When I first read the Original Post here, and began my response, there were no replies (zero). Upon finishing my post, I see that I am number 5. Either I type too slow, or say too much, or both - - oh well!]
Hi Samuraifan and Welcome to MT,
First of all, I would like to congratulate you for embarking on, what could be, a life-long journey in the Martial Art. You will find many people here in the Taekwondo forum of MT to help answer your questions. From the beginner perspective to the more seasoned instructors, there is a wide variety of participants here. Many of us train under different organizations, and have some variations to our understanding and interpretation of TKD related knowledge, but you will likely find many helpful answers and opinions.
One of the most helpful features on this site is the "search" link above which allows you to find the many threads and posts which already exist here at MT, and might answer your questions without having to repeat too much of the same information. However, I do feel that earlier threads might contain the opinions of early participants who are no longer members here, and we have no way of knowing the validity of their experience, or advice in the field of Taekwondo, let alone what is current information. Thus, it is best to do some research first, then ask for clarification or updated information.
I see by your profile that you are already a student, and now you are interested in Taekwondo. I am pleased to hear that. I will try to share with you my insights to what you have asked in the interest of helping you get started.
...I am still unsure as to which one I should start - ITF or WTF.
Your question, which seeks a comparison between the ITF and the WTF, is really not as valid of a question as it may seem. I'm not implying that you should not ask it, because this is how we learn, but this particular question is like comparing Apples to..... a Farmer's Market! There are many different organizations which provide instruction, dissemination of information, rank promotion and certification, access to competitions, among many other things. Some of those organizations are wide-spread, becoming nationally, or internationally recognized with affiliated schools in many different countries.
The ITF, which was founded by General Choi, Hong Hi, is one of those organizations. An individual school or instructor might choose to be affiliated with a large organization, or teach independently, relying on their own, self-appointed authority to teach, and promote students. Any organization, such as the ITF (International Taekwondo Federation), ATA (American Taekwondo Association), or any national or international organization operating in your country, allows schools, instructors, or individual students to join and receive instruction in Taekwondo, and certification of rank.
Conversely, the WTF (World Taekwondo Federation) is no such organization. You can not "join" the WTF, and no schools nor Private Taekwondo organizations are "members" of the WTF. The only members of the WTF are the National Organizations recognized by the WTF for representing the WTF around the world, which help to perform the duties of sport competition and Olympic events. An explanation of this information can be found here:
http://www.wtf.org/site/about_wtf/intro.htm
and here:
http://www.wtf.org/site/about_wtf/member/regional.htm
...So I was wondering if you TKD practitioners can enlighten me about the different aspects of both styles.
Many of us do not consider the ITF, or WTF to be "styles" of Taekwondo, but rather different organizations, with completely different structures, and charged with different responsibilities from different authorities. You might find that any instructor, school, or organization will teach Taekwondo slightly different from each other, but this should not be misconstrued as alternate "styles" but merely methods and individual preferences for providing the same basic information.
Since Taekwondo originated in Korea, Korea is considered the "mother country" and source of authority for training and certification. However, like most all Martial Art education, there are few, if any, legal restrictions on anyone teaching self defense, and calling it Taekwondo or any other chosen name (some terms are coming under copywrite, and might be protected from use without permission).
Organizations operating outside the permission, and authority of the Korean government, and the Kukkiwon (International Headquarters and National Academy for Taekwondo in Korea which houses the KTA - Korea Taekwondo Association) are doing so based on whatever authority (legitimate or otherwise) vested in the founder, and or current president. The ITF was founded by General Choi, a pioneer of modern Korean Martial Art (post WWII era), and the one individual believed to have suggested the name "Taekwon-Do" to be used when unifying the various Kwans (branches or families of Korean Martial Art schools which flourished in the post WWII era).
The ITF is a 'ground-up' organization, meaning that their curriculum is designed to take a student from the ground floor (white belt) to the highest level of Black Belt certification. The approach to teaching, and the over-all curriculum of the ITF is based on the philosophy, knowledge, and authority of the late General Choi, who many consider to have been the "Father of Modern Taekwondo." General Choi was certainly instrumental as a driving force to unify the early Kwans (although not all chose to fall under the "Taekwon-do" umbrella), and he was personally responsible for bringing the Korean "flavor" of Martial Art into the Korean Military which resulted in the ROK Army becoming a fierce and highly feared fighting force.
General Choi was one of many pioneers, and leaders of the early Kwan period (having created his own Oh Do Kwan), and was appointed to many prestigious positions during the late 1940's, 50's, and 60's. He helped to spread the development and interest of Taekwondo around the world due to his many travels abroad in the Korean Military. However, he eventually fell out of favor with the Korean Government, and had conflicts among the other leaders of the Korean Taekwondo organizations, thus he was driven from his positions, left Korea for Canada, and established his own international organization (taking the name of ITF with him). Since his death, the ITF has had a split of perceived control in a power struggle for legitimate authority.
Today, you can join a number of schools and organizations that are members of the ITF, and pursue the Taekwondo experience through their curriculum. Many other organizations based on other Kwan history, such as the first, original Kwan (Chung Do Kwan), or the Jidokwan or other such affiliations offer very similar curriculum. The source of their knowledge, and the authenticity of their training and certification of ranks, is either backed by the Kukkiwon in Seoul, South Korea, or it is based on an independently derived authority which is only as good as the individual instructor's knowledge and abilities to teach. In other words, outside of a major organization, there might not be accurate education, or over-sight by experienced Masters and Grandmasters to keep novice instructors on the right track.
Anyone can teach anything and call it "self-defense," or "Martial Art." However, Taekwondo is a term that implies a specific philosophy, and content of unique skills and application found only in the Korean Martial Art. The ITF is capable of providing you access to this information, and many other organizations in your country can give you access to certification at the Kukkiwon when you reach Black Belt level, but the WTF is an arm of the Kukkiwon which is only charged with the responsibility of the sport aspect of Taekwondo, and has nothing to do with color belt curriculum, nor rank certification (formerly the WTF went hand-in-hand with Kukkiwon Dan certification for Black Belts only, but that has changed).
I hope this helps, and perhaps other members here from various organizations (especially within your own country), can provide details from their perspective.