Yes, you should get the same result. The Kickr will fluctuate above and below the target power but quickly corrects itself with a few seconds. All trainers do this. So even over the one minute steps of the ramp test the overs and unders should cancel. As long as you test with the same power source you use when training, then it is an accurate assessment and a good number to use for your FTP.
I am glad to have seen this topic. Yesterday I got a new indoor bike and it supposedly has an extremely accurate powermeter. So comparing it to the Assioma pedals I noticed the pedals reading 6% too high over a short test when I ramped power from 100W-250W.
But if the bike is reading power at the back, that is exactly the 10W-15W loss from the chain. Makes me feel a bit better again that I did not loose 15W FTP all of a sudden 
That’s good to know, because my basement gets very cold.
Around 200W my Kickr Core reads about 7-8W higher than the Assiomas after the trainer has properly warmed up.
Another data point: my Kickr Core typically reads about 20 Watts higher than my Assioma Uno after a fresh calibration of each.
Yes - I have Kickr core and Assioma duo. Upon using Assioma I discovered my FTP was 22w lower. Or about 8% lower. I think the Kickr core has compensation built in which ends up exaggerating numbers.
I recommend testing using power match and Assiomas before training further if you plan on using your Assiomas as your primary power reading source - otherwise you risk overtraining.
I have always used my Assioma’s as my power indoors and out. I would recommend everyone do that since power match is available.
I’m reading 8-10W lower on the pedals vs my kickr core as well. It didn’t used to be that way though. Just this season. I’ve calibrated a couple times but nothing has changed.
I did the same 4-5 % here 
I compared both.
Assioma Duo registered into Garmin Edge 520 and Kickr Core into The Sufferfest app.
Both spindown and zeroing performed properly before the test.
I saw less than 1% difference for average and normalized power and below you have the overall comparison.
I was pretty happy that I was measuring power based on Assiomas only for outdoor rides.
However, my Kickr unit got electronic problems, and the trainer I bought as a replacement is not showing comparable results. I hope the company will find a way to fix/improve it.
Cheers!
Kickr Core also not always consistent across models. I compared two different Cores on the same day, very similar workout and found that one Core was reporting 3.5% higher than Favero Duo and the other Core was reporting almost the same as Favero Duo.
Just to add a small follow up here… I’ve since been able to compare my Assiomas to a Stages power meter and the Assiomas and Stages were incredibly close—-within 1 Watt most of the time.
Based on this, plus the way power is measured in each case, and having done some reading around, I think my general advice to people who have such a discrepancy is be strongly biased towards trusting the Assiomas.
Probably most people would come to that conclusion a priori, but it’s always tempting to believe the higher number.