When I've been to Ireland, I find that they don't really bother with mushrooms or tomatoes that much, but they do have the wonderful white pudding. Can't really remember them doing fried bread either, they have nice soda bread as well
I've been to Ireland a lot and the the two are pretty much the same, the only regular difference is that the Irish breakfast has white pudding, I've never seen it in England as standard. Otherwise the same.
In Scotland you can get a full scottish breakfast. It's basically all the same stuff wherever you are - a cooked breakfast - it's just called different things. I mean you wouldn't expect a scot to serve up a full english would you?