Your question is similar to another I just answered. To wit:
Those old TVs are analog, not digital, so there's no apples-to-apples comparison, but the equivalent resolution is 520i, as compared to the 1080i that is broadcast in the new digital (HD) format. Keep in mind that the aspect ratio (shape) of the screen is also different. While the old sets were 12:9, the new ones are 16:9.
Many of the older, large-screen TVs are the projection type. If you get a new flat screen TV of the LCD or plasma type, they will not be projection, but direct-view. The advantage of this is a much brighter picture. You will notice this improvement right away. Also, for a few more bucks you can get one of the very new LED TVs, which is even brighter.
Watch out, however, for those DLP type TVs, which are just another projection type. The advantage: relatively low cost for the screen size. Disadvantage: not as bright as a direct-view TV (although they are still considerably brighter than the old projection-TVs).
If you have cable or satellite, you will be able to receive 1080p HD, which is twice as sharp as the 1080i HD broadcast over the air. In this case, you will want to get a TV that is capable of receiving the full 1080p resolution.
Then there's the videos and DVDs you have. Your new TV will make your old videos and DVDs look really good, of course, but you may want to consider upgrading to a Blu-Ray player. Blu-Ray is quickly becoming the new standard for playing full HD movies and videos, and the players are really starting to come down in price, too, don't worry about compatibility; the Blu-Ray player will still play your old DVDs. Then there's Surround Sound home theater. You can get systems for as little as $100.00 or so, or go as high as $1000.00 or more. What better way to enjoy that great action-adventure movie than with a HDTV, Blu-Ray player and Surround Sound?
The bottom line is, if you have the bucks, go for it! I think you'll be glad you did. Merry Christmas!