Really for miners, if difficulty increase hard the price will increase hard too, so you will earn less btc but they will value more...
I have yet to see a valid argument (IMO) that show's BTC price is following diff as you suggest. I have seen a number of valid arguments (again IMO) that show difficulty follows BTC price.
An increase in difficulty does not mean price of BTC will rise, too many other non-mining external factors can push the price up or down. However an increase in BTC price will almost assuredly bring more hash power to the network as mining profits increase.