Are there any permanent job options for students who choose to do CSE over ECE?

There are more job opportunities in CSE than ECE at present. But if we look at the future, I think ECE has a greater scope than any other branch.

I can't say about permanent but yes, there are obviously more jobs in CSE as compared to ECE in the present market. If you work well on your skills in CSE, you won't stay unemployed and it is not that difficult to get into a good firm.