We faced this issue, and it did boil down to logistics for us. We would have loved to keep our son in his Montessori for K. The K year gives the child the opportunity to complete the cycle and be a leader in the classroom, something we thought our son (who has a summer birthday, so he would be a young Kingergartener in a traditional classroom) would benefit from greatly.
That said, we toured private schools, entered the MoCo language immersion K lottery, and visited our local elementary school. In the end, we chose a progressive K-8 private for our son, applied, and he was admitted. Our chances of getting him into the school would have been greatly reduced if we waited until 1st to apply, so we entered him at K. We would have also sent him at K had he received a slot in the MoCo language immersion lottery. Sending him to our local public was our third choice, and if the first two fell through, we would have waited until 1st grade to send him.
We are happy with our decision, but it is by no means a no-brainer. There are benefits of each path.
We did struggle with the decision, and in the end, we went with our gut.
Good luck.