I know it's been a while since this topic arose but I have found the same problem myself and stumbled on this thread.
As it's prominent on Google for someone searching for "best vacuum cleaner for deep pile carpets" I thought I'd add my own take on this.
So, we had a deep pile polypropylene carpet laid last week. Deep and soft, luxurious underfoot.
Got the Dyson (DC03) onto it and it just stuck. Couldn't push it and the belt started smelling and would no doubt have burned out if let running.
So on the advice of others I ordered a Hoover upright with height adjustable head. Not a chance. Same thing. Just clamped itself to the carpet and couldn't push it. Same day return implemented.
Found someone who swore by a Swift 200UK for their own deep pile carpet. They don't do them any more though.
So armed with a large cut-off of around 8ft I made it to Curry's to seek advice.
I tried more or less most of the makes mentioned here, sometimes with newer models if the old one wasn't available, and after much testing which had the Curry's representative scratching his head, I found only the Shark models were up to the job. Not all of them though. The battery operated ones were useless. The brushes in the head couldn't move.
So it was either the 600UK(T) or 800UK(T) which proved best.
They too stuck firmly to the carpet but sliding the vacuum release at the top of the handle across to around 70% open they did a damn good job.
I tried most models in either upright or drag around styles. The Meile was absolutely hopeless despite what others say on here.
I offered to leave my scrap of carpet in the store for others to use when faced with the same sort of problem but for safety reasons they can't do it. I recommend taking some of your own carpet scrap along to see for yourself but in any case I'm more than convinced that the models I say worked well are about as good as you can get.
I went for the 800UKT. It is the same as the 800UK but with the pet hair option and has all the tools with it BUT is around £90 less expensive although the same in every other respect.