Ha! You have put your finger on a source of no end of petty arguments.
I would say for at least 90% of people, there's no difference.
However, some people would draw a distinction, saying "three times as expensive" means "multiply the price by three", but "three times more expensive" means "multiply the price by three AND add it to the original price". So that would mean
Three times AS expensive as £100: £300
Three times MORE expensive than £100: £400
My advice to you is probably to stick to "as" and use it in the sense above, as that's how the phrases are usually understood. But if someone else uses either version, check if you are in any doubt and it's important!
I hope that makes sense - it's one of those areas where there genuinely doesn't seem to be a "right" answer, as far as I'm aware.