Connection speed and wireless range have never been a problem in the two years since I switched to BT and got a HH5. What initially was a problem was its tendency to drop its connection sometimes several times a day. I fought with the BT noHelpline (who are always overseas with a poor grasp of both English and the subject matter) who blamed it on my phones and interference from the house's additional socket, even though it was installed by a BT engineer. Presumably the average IQ of their customers is about 46 if this fobbing-off makes most complainants go away. Only when I threatened to remove my custom just a month into the contract did they get it sorted. It still drops off a couple of times a week. But that's a huge improvement on how it was.
The answer would appear to be cable, but I'm part of the 50% of the population which doesn't have it, and probably won't get it 'til hell freezes over. They had a blitz on cabling my area in the late 1990s, getting within 250yds of my house in every direction. Then stopped. And that's the way it's been ever since.