I actually find that US-04 has a little twang to it. I can't describe it well, it's not a phenolic, just a little estery. I've fermented it cold (62*), and it's still there, so I gave up on S04. I use WLP007 for my Dry english needs.
I find that it has a twang too...at least while it's young. It tastes sort of like soured oak. A buddy of mine once brewed an English Brown with it which he didn't like very much for the S04 taste. He left a few in my fridge and somehow I forgot about them for a month. A month later I found them sitting at the back of my fridge and poured him a glass without him seeing. He couldn't identify the delicious brew he was drinking and was totally shocked to find it was his own. I think S04 just needs a little more time than other yeasts to shake off its green flavour, but when it does...so good!