"Regular" or academic kindergarten typically involves more direct instruction of math, reading, writing, and science skills. The focus is on the acquisition of specific academic skills, such as reading and adding numbers before first grade. There are many advantages to academic classrooms, but they have been criticized for their intensity and focus on academic skills. Many parents and experts claim that students still need time to "play" and learn about the world around them through more informal learning. Therefore, younger children are sometimes held back a year if there parents have an option when an academic classroom is awaiting them.
"Developmental" or "child-centered" kindergarten, on the other hand, involves a focus on inspiring a love of learning. Learning is still a big part of developmental programs, but it is learning in a more general sense. The organization of the physical space is very important and students learn through engagement with sand boxes, crayons, and other items in the room. In general, students are steeped in "experience" and learn through their senses. In addition, communication and social interactions are valued and important.
The article below discusses the differences in more detail (pay particular attention to the second page).
Consider all of the information available to you, but do not forget to use your instinct, too!
L. Compian, Ph.D.
During the first three to four years of Elementary school there is quite a bit of variation in children's understanding and performance of reading and math concepts and skills. For example, some children start Kindergarten with the ability to read, others are learning to recognize and sound out the alphabet. This is all normal and reflects the great variation we see in young children based on how their brains and bodies are developing.
A developmental Kindergarten program recognizes the natural variation in children and emphasizes the unique progress that each child makes from the beginning of Kindergarten to when they complete Kindergarten. Many public schools under the No Child Left Behind act emphasize that children all meet a certain level of performance in core subjects like reading and math by a certain time.
Also some school districts have Young Five's or Developmental Kindergarten programs for younger children (turning five between July and December) or those needing the "gift of time" to develop socially, emotionally, and academically before entering "regular" Kindergarten.