I'm in Aussie Land so can't speak for the A roads in the UK, but I think you will find the H2 completely different to anything else you have ridden.
Yes it is a heavier bike than you previous bikes, but I find that bikes nowadays are fairly close in handling corners regardless of weight/size in this category. You will find it doesn't hold a line as well as your BMW or Yamaha did, but not by much. Really depends on your riding style/capabilities. There are a few blokes on here who regularly track ride the H2 and have sorted the suspension etc. out such that it holds its own on corners with other more nimble bikes. I am starting to do more track days on mine (got a 3 day track ride at Phillip Island booked for second week in December, and have done that track once before and once on the new "The Bend" track at Tailem Bend here in South Aust. couple of months ago). Not saying you have to do the track though!
Personally, I have found the H2 to be a joy to ride every time I'm on it. It is well made, and gives a level of performance you will not find on any other bike, currently.
Enjoy the bike, and I look forward to your thoughts on how you find it!