Brain Teaser: How well can you trust your intution?

Intuition can be a powerful guide for solving problems, but sometimes it can lead us astray. This problem is based on one from Project Euler

Let us say that a number has an ascending digit sequence if, writing the number from left to right, each digit is greater than or equal to the previous one. For example, 234 and 788 would have ascending digits. Define a descending digit sequence analogously. 855 and 210 would be descending sequences.

Now consider the numbers from 1 to 99. For one and two digit numbers, every one is an ascending or descending sequence. What does your intuition tell you about the comparative number of ascending and descending sequences? Are there the same number of each or are there more of one than the other? Was your intuition correct?