The Yoga styles I've been exposed to;
Iyangar - Very strict, emphasis on holding postures absolutely correctly and for long periods. Developed by VKS Iyengar in the 1950's. Tend to use props (straps and bolsters) to help you achieve the correct posture, then gradually take the props away as you improve. It's amazing how many Iyengar instructors are Swiss or German - 'You vill hold zee leg strait'.
Hatha - More generic style, emphasises easier postures and breathing.
Astanga - vet gymnastic. Flows quite rapidly from one posture to another. A great high if you are advanced enough to do it.
Bikram - Yoga done in hot rooms to generate greater cleansing and blood flow. Very smelly but you do stretch a long way.
Kundalini - a variation on hatha yoga which focuses on aligning energy flows. Slightly more mystical and esoteric. Might push a few of your buttons if you are a Christian, although it shouldn't because the purpose of Yoga is to clear your mind to allow you greater communion with your god, whomever that may be - not to be a religion in itself. Some instructors do forget this important truth.
It's a little like martial arts in how different styles are invented or blended from one to another and different people espouse of their style as the 'only way' (Iyangar followers are particularly guilty of this snobbery)
Check out this site if you want to do some reading.
http://www.yogasite.com/yogastyles.html
From personal experience, having dabbled with Yoga for 5 years and noticing my dedication increase over time, I can espouse the following benefits.
1) Weight control - Although running and high intensity exercise will drop fat faster. I have lost weight steadily in the times I was doing Yoga alone. This supports the growing idea that a stressed body/mind will store fat more readily and lose it more slowly. Yoga drops your anxiety levels remarkably, taking your body out of that alarm state where it tries to store fat.
2) Stress/Anxiety - This is the reason most people try Yoga to begin with. Most exercise will improve your sttress levels but this is where Yoga particularly excells.
3) Real world fitness - On some of my adventures I have had to crawl, scramble, climb and generally be a monkey - since I've been doing Yoga I am far more effortless moving through a natural environment. This is somehting that a few of my compadres have noticed in the last few years. How I move easily where they are grunting and straining.
4) More mental energy - I've noticed in writing and working with clients I get less drained by 'work' and seem to have a more abundant reserve of energy.
5) Feel younger - In the years when I was playing football and doing Triathlons it seems that feeling stiff and sore in the mornings was part of my life. Now I notice that I spring out of bed in the morning.
6) Better sexual performance - I'm not kidding. All that muscular endurance, flexibility, body control and stamina does have it's uses.
7) Did I mention that their are some lovely women who do Yoga? Down to earth, intelligence, non materialistic and fit.