To properly discuss judo's benefits as a martial sport as compared with other sports and martial arts, we must first define some terms.
What is the difference between a sport and an art? A sport is any physical activity undertaken primarily for the personal enjoyment gained from exercising one's body or from competing with others. An art is any activity in which the major goal is, depending on whether the art is focused on creation or performance, either self-expression or the quest to improve one's skills in that art so as to approach perfection in execution. In a performance art, the goal of perfect skills execution can almost never be achieved even by the most skilled/talented, but personal satisfaction can be gained via consistent improvement and competent (if imperfect) performance.
There is obviously therefore much overlap between sport and art. An artist seeking to improve his or her technique will usually compete in some way with his or her peers. Likewise, a sporting competitor will constantly seek to improve and refine his or her performance in order to win. Everyone who watches ballet or ice skating knows that performance artists regularly execute great feats of athletic skill, and everyone who watches sports such as football and basketball knows that athletes can perform moves of great skill and artistry.
However, it should be noted that martial arts occupy an odd niche in this scheme. The martial arts require a high degree of skill, and many martial arts maneuvers are quite graceful and beautiful. However, unlike other performing arts which focus on beautiful movement and self-expression, the martial arts are highly goal-oriented, and that goal is to destroy, not create. There is little if any goal of self-expression involved in most of the martial arts (though one could consider the act of convincing an attacker to run away to be valid self-expression). However, many martial arts styles have a heavy focus on spiritual development and enlightenment; this element is absent in other performing arts. And in the martial arts, all physical effort is put toward developing practical skills of self-defense and attack. In light of the martial arts focus on practical skills with beautiful movement as a by-product (a highly valued one in styles such as kung fu and capoeira, true, but still secondary to the practical goals of being able to hit, throw, etc. effectively), it seems that the martial arts should instead be called martial crafts (this, of course, is in line with the closer translation of martial arts as "martial ways," but in this country "art" sounds more appealing than "craft").
The martial arts can be further broken down into two categories: martial arts and martial sports. Martial arts such as kung fu and hapkido focus entirely on developing skill for the sake of self-defense, self-improvement, and spiritual enlightenment. Martial sports such as judo focus mainly on the development of skills for the sake of winning competitions (though they do focus on mental training). And some styles blur the line: karate, aikido, and taekwondo focus on self-defense to a great degree, but in many styles students are expected to test themselves in tournaments against other students.
So, how does judo compare to other martial arts? And how does it compare to other common American sports?
Because all martial arts focus on self-defense, and because there are so many styles in existence that it would be impossible to compare judo to even a fraction of them, let's compare judo to U.S. Hapkido Federation-style hapkido, a highly practical, jujitsu-like Korean art.
Both styles have roots in Japanese jujitsu of the Edo period, but since then they have diverged. Sport judo teaches throws (via unbalancing and using leverage to hurl one's opponent to the ground), leg sweeps, and ground fighting (pinning and locking). Hapkido students likewise learn throws (via a combination of unbalancing and applying joint locks that make it more pleasant to the opponent to go down than to resist), leg sweeps, and ground fighting (pinning, locking, pummeling and limb breaking). However, hapkido also teaches kicks, strikes, blocks, the aforementioned joint locks/breaks, and weapons teachniques (baton, staff, cane, nunchaku, etc.)
The focus in hapkido is on kicking, striking, and joint locking, especially at the lower ranks. Because of this, a lower belt judoka will likely be far more proficient at throwing and falling and will have a better ability to use his or her body weight and leverage to unbalance an opponent. However, while that same judoka will have attained physical abilities that will aid him or her in a self-defense situation, the hapkido student will likely be much better prepared for real physical conflict and will be able to stage a wider, more effective range of responses.
Another issue is the relative strenuousness of the two styles. Because hapkido focuses on joint locking/breaking, there may be many class sessions where students do not engage in strenuous cardiovascular activity. Judo is highly strenuous, and excellent for building muscle tone. Because of the physical benefits and the extra focus on throwing and ground work, judo would be an excellent cross-training activity for the hapkido student. After all, hapkido hapilly encompasses a wide range of techniques, and if the student learns a useful new maneuver in addition to improving his or her physique, so much the better. Likewise, judoka who wish to really learn practical self-defense techniques would do well to take some hapkido, as long as they can remember not to inadvertently use it during a judo match.
So, how does judo compare with other American sports? Unlike many sports (e.g., tennis, bicycling, baseball, etc.), it is an excellent all-round strength, endurance, and flexibility developer. And because so much of a judoka's early training focuses on safety techniqes, the sport is actually safer than sports such as football, basketball, hockey, and roller blading. Furthermore, as mentioned before, students do learn some level of practical self-defense skills. However, many people may find the apparent violence inherent in the sport to be off-putting. Likewise, a weak or poorly conditioned or uncoordinated student (whose physical skills would improve greatly from learning judo) may try the sport and then quit after a few sessions out of a feeling of discouragement and inadequacy (thus, the compassionate judo instructor should watch for these students and provide them with extra encouragement and technical advice).
Judo's closest analog is wrestling (both freestyle and Greco Roman). Both sports benefit players with increased strength, endurance, and flexibility, and both are Olympic competitions (judo became an Olympic sport in 1964). However, unlike wrestling, women can participate in judo (though the high level of body contact may make mixed gender matches uncomfortable to the players). And because judo is a more "stand-up" style of grappling than Western wrestling and relies more on leverage than brute strength, judo is (usually) less damaging to the back, knees and other joints. Both wrestlers and judoka attain a measurable level of practical self-defense skill. However, wrestlers are generally only given opportunities to compete in high school and college, whereas judo dojos are available to all ages. And finally, judo involves mental training, (and, depending on the dojo, even spiritual enlightenment) that may serve the player well long after he or she has stopped competing.
Burns, Donald J., An Introduction to Hapkido: A Teacher's Manual. Collegiate Copies. 1994.
Burns and Thompson, An Introduction to Judo for Student and Teacher. Kendall/Hunt, 1976.