So there are many experts advising you as to which one is better/easier than the other, but let me set the record straight by sharing my results in both the exams.
The reason why I rewrote the exam is just to improve my score under the Express Entry. I think of my skills as average and most of the exams I wrote was while working full-time and with less than 3 days of preparation. CELPIP uses a different scale exactly similar Canadian Language Benchmarks (CLB) so I will tell you what was my IELTS worth in terms of CLB scale which Express Entry accepts. FYI if your score is a CLB 9 (IELTS L - 8, R - 7, W - 7, S - 7) or above your express entry score really gets boosted.
I took the exam 3 times each at different occasions with in the last 1 - 1.5 year just to achieve an overall CLB 9 score and above. I have added the info below.
1) IELTS 01-AUG- 2015
L - 6.5, R - 5.5, W - 6.5, S - 7.5 i.e (CLB scale conversion L - 7, R - 6, W - 8, S - 10)
First time I wrote the exam, found it to confusing as I did not prepare much for this.
2) IELTS 12 -SEP- 2015
L - 8.0, R - 7.5, W - 6.5, S - 7.5 i.e (CLB scale conversion L - 9, R - 9, W - 8, S - 10)
Went in with much more required preparations, tried as hard as I can, Damn writing got me off guard, if I would have got 7 in writing my score would have boosted and I would have to never write CELPIP.
3) CELPIP 07 -NOV- 2015
L - 12, R - 7, W - 7, S - 10
My friend introduced me to CELPIP, we tried the free test, we loved the listening, reading and speaking session. We thought we easily excel in this. Turns out we did not change anything.
4) CELPIP 19 -DEC- 2015
L - 11, R - 12, W - 8, S - 8
For this one me and my friend shared the CELPIP-General online practise 3 test set (CAD $75) was expensive, but we still couldn't crack the writing. Speaking score fell due to them introducing an additional part 8 which was very underdeveloped. it was something really random to locate a boat and talk about it. I had no idea what they were referring about, I knew I messed up speaking part.
5) CELPIP 23 -APR- 2016
L - 10, R - 10, W - 8, S - 8
By now I knew for a fact that me doing anything would not change my score and gave up at this point, waited till JAN 2017 to receive an invite with my second attempted IELTS score. To my surprise after I got the invite they asked me to use the latest score. I was heart broken again, decided to decline the invite and one last time write IELTS.
6) IELTS 16 -FEB- 2017
L - 8.0, R - 8.5, W - 7.0, S - 8.5 i.e (CLB scale conversion L - 9, R - 11, W - 9, S - 11)
This was my best attempt so far, studied for it for a week with full determination and thought about how I will get kicked out of CANADA soon. My Express Entry score sky rocketed
My analysis, write IELTS don't debate between these two. My reasoning? Its is simple CELPIP is still in its developing stages, 2 categories where they can really control is writing and speaking hence they marking is really hard. Other categories (Reading and Listening) they cant control the answers, there is no grey it either right or wrong. IELTS on the other hand is developed and they mark everyone equally, they don't have to prove their legitimacy that there are a standard international exam, celpip need to do that!
Few other tips, write IELTS in a place where they are less people and preferably different nationality then you are, this in my experience really helps change things up for speaking. This might sound crazy, but you doing excellent from good has a lot to do with luck too. I wrote my last exam at William International School Toronto, less people and they have big tables where you really feel comfortable when it comes to writing. I don't think it has anything to do with my sudden knowledge for grammar or English vocabulary.
Good luck Everyone!
Links for what I spoke about.
http://ieltscanadatest.com/test-results/ielts-and-clb/
Check your score here -
http://www.cic.gc.ca/english/immigrate/skilled/crs-tool.asp
Hope this helps you taking a wiser decision when selecting one of the two.