The answer is: ripe chillies are hotter than unripe chillies. I am yet to hear of any exceptions to this. If you know of a variety that is an exception to this please let me know as I would love to grow it.
Ripe chillies tend to have higher sugar content, so sometimes in mild varieties it may be easy to overlook the heat, but ripe chillies are still hotter even if they are sweeter.
I have some varieties of chilli that I can happily eat raw when unripe and feel absolutely no heat, but when they are ripe I feel like I have been stung in the mouth by a bee.
I also did a little searching on the internet and found proof to back up what I have experienced. Below is something I found on a chilli forum, hopefully the person who owns this picture does not mind me using it. I have linked to their thread so I figure that should be ok. With Scoville Heat Units, the higher the number the hotter.
Apparently 25 unripe chillies and 25 ripe chillies were picked from the same plant and analysed. The ripe chillies came out about twice as hot as the unripe ones. I think that it is pretty conclusive.
|SHU comparison from http://thehotpepper.com/topic/62026-whats-hotterripe-or-unripe/?hl=%2Bheat+%2Bripe+%2Bunripe|