In practical terms, the difference between a SD broadcast - like NTSC - is as noticeable as the difference between setting your monitor to 800x600 or 1280x1024. To some, very, to others pedantic and meaningless since you can see the content in each.
You do need some expensive equipment to achieve the top marks in terms of potential quality - like a Full HD TV, a Blu-Ray player (the most prominent of which currently being the PS3) and an HDMI cable or quality equivalent component. The fact that most people don’t notice is because most retailers still sell a lot of middlware, like so-called HD Ready TVs (which display in 720p or 1080i, IIRC, unlike full HD which display in 1080p) and so the leap seems more like a phaze-out. One of the nice things about these standards is the fact that the signal is going over to digital HDMI, in which the low-line cables deliver within the range of very few percent - unnoticeable - of the high-range, expensive ones.
To quantify it, I would say the leap between DVD and HD-DVD/BR is as big or bigger than the quality leap between VHS and DVD.
If you want in on BR, the best advice I can give you would be getting a PS3. Aside from full 1080p support it’s also the only player out there that I know has BR Profile 2+ on it, which is an interesting feature. It’s also relatively cheap as BR players go.
(BR Profile 2+ can download and update content on a BR disc you have. Say, for example, you get the Dark Knight on Blu-Ray when it comes. They’re in the works with the third film in the trilogy; you could easily be offered exclusive sneak-peaks, teasers and trailers as an owner of the Dark Knight BR, if you have it in your disc. Or they could release extra bonus material over the course of time and so on.)
ETA: To go to the technical side of things, the DVD has achieved its max capacity of data: around 9,4GB on a Dual-layered disc. The theoretical limit of the BR disc is 200GB on a multi-layered disc. The entire Lord of the Rings discography with bonus content discs in SD would take up just above half such a BR disc, rather than 12 DVDs.
This also means that we will in the close future may be watching uncompressed film, which will do miracles for the quality.