What kind of take off do you use for the Kong? Split foot, double punch? That could be it. Some people find the double punch gives them great height but takes away forward momentum. And most people say the split foot is the best for distance. I personally use the split foot almost all the time, even for Kong to precisions.
But since you are having trouble when the wall is the same height it may be your precision technique and landing skill. For a while I could only land 100% of the time to a lower bar, parallel height about 40% and jumping to a higher rail was 10%. I trained precisions and balance allot and there are allot of precision tutorials out there but I found that I would go too far forward and not up. Most people tell you to jump at a 45 degree angle but for me it’s 30 or so. If you perfect your precision landing you will be more successful.
A friend I have been training is scared of the Kong to precision and so instead of keeping his legs tucked after the Kong he drops one in case he falls but that pulls his momentum down, try and see if you do that. Keep your knees tucked and at the last moments reach your feet out as you spot the landing.
I think if it was me though I would work on the proper take off of the Kong. Practice your kongs somewhere else and try to get high and far, like I said I found the split foot method to work best for me. I hope I helped, if not post a video of you attempting it a few times so we can get an idea of what you are doing.