I'm a bit biased since I only collect Japanese cards that are in the first edition, but yeah, first edition is still important with Japanese cards. 1st edition boosters are only sold for the first month or so in Japan. After that, they print the unlimited edition pretty much until the format is updated (i.e., BW-on, etc.). In the long run, first edition is definitely worth more than its unlimited counterpart. What is funny is that (someone correct me if I'm wrong) Japan did not have first edition sets until the Pokemon VS set and America stopped having it around EX Ruby and Sapphire. So yeah, first edition is definitely a plus. It makes the collection more rare, if you will.
Also, just a side note, American cards do not explicitly say "1st Edition" anymore, but the reality is that there are still times when our sets have a "first edition." The only two examples I can think of are PokeBody Empoleon Lv. X from Diamond and Pearl (which was supposed to be PokePower) and the two different versions of Zekrom FA from the Black and White set.