The dome (aka the millennium experience) was a failure because there was no clear idea what it was for. It ended up as a random pile of exhibits which showed the very worst in high-mided 'creative' intent. It's only been successful following its retooling as a concert and sports venue.
By contrast HS2 is very clear what its purpose is, that is to provide much needed additional north-south rail capacity, the extra speed being a useful by-product. My opinion is that HS2 will be a resounding success. Peak fares on long distance services are astronomical, yet the trains are still full. To me this shows there is massive constrained demand which HS2 will be able to satisfy with its economies of scale (1100 seats per train, capital cost of trains spread over more services etc.)
Unfortunately this fairly simple concept has been poorly communicated by HS2. They have produced a lot of good, solid, detailed reports explaining this, but have singularly failed to engage the majority of the public who aren't going to read long reports unless they have a particular interest in railways and don't use trains much (the average number of long distance train journeys per person per year is less than one, apparently). As a result most people don't see the problem HS2 is planned to solve, and swallow the oft-repeated rubbish eminating from the anti-HS2 groups. HS2 haven't made a very good job at countering this. Hopefully this will change under new management.
This is turning into a mild rant, but recent journeys on Crosscountry have convinced me more than ever that HS2 is essential. An 'Intercity' service trundling between Leeds, Sheffield, Derby and Birmingham, stuck behind slow trains cannot be the future.