Here's my experience with both exams.
I decided to try CELPIP first because it looks like TOEFL ibt (computer based), which I have tried 8 years ago.
My goal was CLB 9, so my first CELPIP was in mid July 2018.
I scored 11 Listening, 9 Reading, 7 Writing, 8 Speaking. After re-evaluation, my writing changed to 8, but speaking stayed the same.
Then, I took IELTS one month after. My score came back at the end of August. It was 8 Listening, 7 Reading, 7 writing, and 8.5 Speaking.
My results look funny if you compare my speaking scores. (8 in CELPIP and 8.5 in IELTS?????? Really??)
My friend also scored 8 and 8 on CELPIP (speaking and writing), so she tried IELTS the same day as I did, and got her CLB 9 as well.
I have never heard anyone who got 9 and 9 in speaking and writing at the same time in CELPIP from my study group.
I was lucky enough to be able to try both exams, and passed my IELTS with only one try.
Please try IELTS.