The main differences between the two editions are the type of binding and the number of illustrations.
The first book that you linked is the 2004 HarperCollins hardcover illustrated edition. The second is the 2008 HarperCollins paperback illustrated edition.
Both of these use the 2nd edition text, include the new forward by Christopher Tolkien (quoting from Tolkien's Letter to Milton Waldman), and are illustrated by Ted Nasmith.
Here are the differences:
2004 HarperCollins hardcover illustrated edition
- Hardcover with dustjacket
- larger dimensions and weight
- The Map of Beleriand and the Lands to the North is colored by H.E. Riddett, and printed on the endpapers. (In the first impression of this edition it was a fold-out, but I'm assuming if you're buying it now, you're getting the later impressions.)
- 45 color illustrations from Ted Nasmith are included
2008 HarperCollins paperback illustrated edition
- smaller dimensions and weight
- The Map of Beleriand and the Lands to the North is printed in its original black and white and spread over the final pages.
- 16 color illustrations from Ted Nasmith are included
It is now nearly ten years after you've asked this question, but if you still haven't made your decision by now, I'll say that the hardcover edition is a nicer book, but otherwise is effectively the same thing and so if you just want to read it for cheap you'll be fine with the paperback.
(Also the 2021 Hardcover illustrated edition is superior to the 2004 one, so if your goal is to have the nicest copy just skip that edition.)