Hi Mike,
If I may be so bold as to speak for all of Baguazhang (LOL), I’ll try to explain it a bit. The name means Eight Trigrams Palm and is a reference to the eight ‘gua’, or trigrams, which are part of the mandala known as the Bagua. This mandala, or symbol, is associated with Taoism and also with the I Ching, the classic Book of Changes. Baguazhang is a truly Taoist art through and through.
The origins of the art are shrouded in mystery (would we have it any other way?). The first well-documented practitioner, and possibly the art’s founder, was Dong Hai-chuan. Dong supposedly was trained in local Shaolin-based arts before beginning a study with Taoist monks. These monks taught him their ancient practice of circle walking, which is a staple of all Bagua variants, and which he incorporated into his fighting methods.
Dong came to Beijing, either to seek his fortune or to escape prosecution, depending on the story, and supposedly landed a job as a glorified waiter for the Imperial Court. His deftness at moving in and around the busy court while serving attracted the attention of the Emperor, who called him over for a demonstration of his abilities. As the story goes, he made such an impression that he was offered a position training the Imperial Bodyguards in this new art. Dong’s first generation students were all well-trained in other methods before studying with him. Dong encouraged this diversity and as a result, today’s Bagua enjoys quite a bit of stylistic variance.
As a whole, the art is known for preferring open-hand strikes to punches, circular or spiral movements, and constant flow and shifting of direction while in combat. Taijiquan, XingYi Quan, and Baguazhang are commonly known as the Three Sisters of the internal arts, or neijia. Of these three, Baguazhang places the strongest emphasis on chan siu jing, or coiling energy, and also on rooting while in motion, though all three arts share basically the same principles overall.
Bagua practitioners were known for their lightning speed as well. The two factors which most strongly contributed to this are its unparalleled fluidity of motion and its strategic use of body positioning and footwork. Bagua fighters were known for getting around behind an opponent before he realized what was going on. Not to say that they were excellent sprinters, but rather that they were often able to combine nimble side-stepping with turning the opponent’s body as a counterstrike.
Personally, my first impression of it was that it was like Aikido, only with teeth LOL. I was also amazed at how quickly an opponent could be completely debilitated from head to toe. Bagua is known as a ‘soft’ art in the U.S., but this is often a misnomer. ‘Soft’ actually refers the fact that a Bagua fighter never meets force against force as in a typical Japanese style hard block. Also, it refers to the flowing nature of similar arts. Bagua, despite the ‘soft’ label, is one of the most brutal and devastating arts I’ve encountered in 26 years of training.
The book you referenced (for that matter, ALL books on the art in English) doesn’t even begin to properly represent the art’s effectiveness in combat, though that particular book is a must-have for all Bagua practitioners. It contains an excellent history of the art, as well as an exceedingly rare collection of Bagua poetry. While the form demonstrated in the book is good, the applications are as overly simplistic as they are sparse.
IMO, there just ISN’T a book available in English which really does a proper job of conveying the art’s fighting applications. The closest might be John Bracy and Liu Xing-han’s book, ‘Bagua’.
As for Bagua’s similarity to Taiji, other than being one of the Three Sisters, I suppose it would depend upon which variant of Taiji you have been exposed to. Taiji ranges from the fajing-heavy rapid-fire lethality of Old Yang Lu-chan style to the anjing-heavy evenly flowing large circles of new Yang Cheng-fu style, with other variants somewhere along the spectrum in between. Bagua has elements in common with all of them, to a degree, given that it contains a wide range of available responses to an attack.
Perhaps Sun style Taiji is closest, having been developed by Sun Lu-tang, a master of all three sister arts. Sun’s stated intention was to blend elements of all three arts into his version of Taiji, so it already contains Bagua aspects. By far, most of the Taiji in the U.S. is new Yang Cheng-fu style. Often it is presented as a tool for health development, typically for the elderly. It is also quite popular with the New Age community as a pathway to enlightenment. IMO, this version is a far cry from the art used so effectively by Yang Lu-chan, the Invincible, as instructors typically don’t know much about the actual combat applications of their art.
Back to Bagua though, I have more than once had it mistaken for the Indonesian art of Kuntao, another art known for its extreme brutality. Unlike its sister Taiji, Bagua hasn’t suffered the same watering down process yet, and still retains the fullness of its martial character. I sympathize with the uninitiated onlooker trying to discern what makes Bagua a fighting art when watching a Bagua student walking the circle performing palm changes. It can be mesmerizingly beautiful to observe, with the practitioner constantly twisting, turning and changing direction, all while flowing seamlessly from movement to movement. It can also be equally perplexing when trying to determine how such movement would be of much use in a real fight. Such mystery adds a bit of spice to practicing the art.
Anyway, please forgive the length of this post, but I hope you liked the 25 cent tour of the art of Baguazhang. There are quite a few practitioners of it on this forum, and while we may not all agree on the particulars, I’m sure we’d be more than happy to try and answer any further questions you might have. 
Chri