Before trying either of these martial arts, I urge you to perform your due diligence and research the instructors, their lineage, and visit potential schools a few times before committing. You should feel comfortable as you will spend a great deal of time and money getting in shape, improving self confidence, and developing relationships on your journey.
Brazilian Jiu-Jitsu — I know some of you hear this and think samurais and ninjas, but BJJ is a lot different. BJJ is dubbed "The Gentle Art" and is sometimes called Gracie Jiu-jitsu after the family that evolved this style from Japanese jiu-jitsu. It was made for the smaller, weaker people to be able to defend them against a larger and stronger attacker by using leverage and technique. The best way to describe BJJ is like human chess. There is a cerebral approach to practicing because if you move before you think, you can be swept (put in a defensive position) or, worst yet, caught in a submission (a position of defeat). Your plan of attack or sequence of moves must be thought out before you actually do it. Meanwhile, your opponent is doing the same. It makes for a fun "cat and mouse game".
There are two types of schools: self-defense and competition or sport BJJ schools. Self-defense schools follow the traditional (original) curriculum. It may be difficult to find these school because sport schools are more popular. Sport BJJ schools utilize traditional and newer techniques that emphasize positions and moves that score points in tournaments. In a typical BJJ class, you will perform a cardiovascular warmup for 10-15 minutes. During this time, you may jog, perform calisthenics, and do some active flexibility exercises. Then the instructor who is commonly called "Professor" will show two or three moves / techniques that you and your partner will spend 15-20 minutes drilling. From there, you will do light sparring with multiple partners and try different techniques and sequences of moves. BJJ will improve your cardio, flexibility, and grip strength.
Muay Thai kickboxing or Thai boxing is one of the national sports of Thailand. It is called "the art of 8 limbs". In Thai boxing, the participant will use his fists, elbows, knees, and feet to strike an opponent. The beauty of this martial art is in its simplicity. Unlike BJJ, which has hundreds of techniques, Thai boxing only has a few dozen. The hours of honing technique and timing is what makes Muay Thai effective. There is nothing gentle about this sport. The techniques, specifically the kicks that are done with the shins as opposed to the feet like other martial arts, are extremely powerful and cause tremendous damage to an assailant or opponent. Thai boxing will improve cardio, flexibility, coordination, and speed.
Dr Rawle Shewprashad