Yes, Blu-Ray has proved to be a better alternative to HD-DVD. Blu-Ray has better capacity than HD-DVD did, and as such, it is able to provide 1080p playback with ease. The only thing HD-DVD had going for it was that it had the initials "HD" in its name back when HD televisions were first becoming available.
The mere fact that Blu-rays are still around should be an easy way to answer this question. Blu-rays did not stick around off of sheer luck, they were clearly the better choice when both were on the market. Blu-rays hold so much more data than HD-DVD's that it is not hard to see why they overtook the market.
Yes, BluRay discs are a better alternative to HD-DVDs. That's the reason BluRay was made into the next generation DVD standard and HD-DVDs were not. It's been so long now that no one is making HD-DVD players or discs any longer. BluRay is here to stay, at least until something better comes along.
I do not think that Blu-ray discs are a better alternative to HD-DVDS because I do not even notice the difference between the two. Maybe if I had a TV for that purpose alone I might, but as it is now I see no difference between them. I think they are just more expensive.
No, Blue-Ray discs are not a better alternative to HD-DVDs, because there is not a sufficient quality difference between the two. A person just has to purchase the one that will work with their operating system. But neither one is really better than the other. They both play DVDs in a fine manner.