In my experience, writing in a public channel gets slower responses, if any. Especially if nobody knows the exact solution to your problem. Some people don't have notifications enabled for group chats / public channels, and even if they see the message they may think "someone else will reply".
Asking someone directly almost always results in a quick response, even if it is a "I don't know" answer. And an "I don't know" from a senior colleague can mean a lot, for example that the problem is much harder than you initially thought.
