Yoga stretching puts an emphasis on your breath and your body position, while regular stretching can include static stretching (what you used to do in gym class) and/or dynamic and ballistic stretching, which can involve bouncing while in the stretch. Regardless of which one you choose, just know that a little stretching can save you a lot of pain in the long run.
Pros of Yoga Stretching
Yoga stretching teaches you to focus on your breathing so that you don't hold your breath while stretching. Yoga also requires you to pay attention to the way your body is aligned while you stretch. This emphasis becomes so ingrained in practitioners that breath and alignment awareness are usually carried over into other exercises and everyday life. Yoga also exercises the smaller stabilizing muscles around the main muscle group that is being worked, to give a more inclusive stretch to the body.
Cons of Yoga Stretching
Practitioners sometimes get so caught up in sinking into the pose that they push too far, too fast. This can easily happen in a class setting if the instructor or yogi does not explain modifications for those who are just beginning or who have physical limitations from illness or injury. Another problem in yoga class can be that people get caught up in trying to stretch into the poses as deeply as the person next to them. Competitive stretching should be avoided, because there are some people who are naturally very flexible and trying to out-stretch them can cause injury.
Pros of Regular Stretching
Good old fashioned gym class stretches (such as grasping your foot and bending it behind you ending up with your heel touching your behind) are so familiar to people that those are the stretches that average folks do when they bother to stretch at all. Since these types of stretches require little to no supervision to perform, they are accessible to everyone. These types of stretches are not intimidating and therefore are more likely to be done by those who are new to the world of stretching.
Cons of Regular Stretching
We have all seen runners with a leg propped on something and bouncing into the stretch. For years it has been thought that this is the biggest drawback to regular stretching, because the bouncing can supposedly create tiny tears in the muscle. Despite some arguments that bouncing doesn't cause harm, the general consensus is still that good old fashioned bouncing can cause damage. So to be safe, just stretch it, don't bounce it.
As with most things in life, it boils down to personal choice when deciding between yoga stretching or regular stretching. Just keep in mind that if you choose the yoga route, you need professional guidance in the beginning, either from an instructor in class or on a DVD. Likewise, if you go with regular stretching, remember that the most important thing is to go slowly with even movements and leave the jerking motions back where they belong, in high school gym class.