I haven't been playing Arkham Horror comparatively long, but I've been playing it quite a bit since I picked it up for the first time 6 months ago. I've already bought most of the expansions (I passed up the last remaining one, Kingsport in favor of Elder Sign, but I'll finish my collection soon!) and I've put a lot of time into Arkham Horror games. Granted I still get some of the rules wrong, but Arkham Horror delivers a unique half RPG/half board game experience that I just love to death.
Elder Sign does not deliver the same experience.
But the experience it *does* deliver is every bit as fun as Arkham Horror, but in different, but equally good ways.
Part of Arkham Horror's uniqueness is in just how difficult a game it is. The game hates you, wants you to suffer, and laughs at your pitiful efforts to thwart it. It makes for an intense gaming session where even just one game will take hours and usually leave you feeling exhausted afterwards. There's a certain beauty to that play style that makes Arkham Horror worth playing.
Elder Sign, in contrast, merely dislikes you. It's enough to make it not a guaranteed win, but you never feel like the game is somehow sentient and finding ways to specifically screw you over. While your victory chances in Arkham Horror get to around 50% (at best), judging by my first few games of Elder Sign, your chances of winning are more around 75%. The game won't do anything to make you glare at it with hate and loathing which can actually can be a plus. It won't make it boring either, as those darn die have a habit of not ever rolling what you're going for (I once got all spell Icons on the sole mission that had no spell's whatsoever. DOH).
Arkham Horror is unique in just how immersed you will feel in the setting. Elder Sign could not replicate that fully, but it does a good job of giving a sufficient feel for the theme. There's more lore on the missions and monsters, which doesn't quite make up for the Encounters, but does fine for its size. If you want a quick fix of Lovecraftian Horror, Elder Sign fits the niche perfectly.
But by far Elder Signs biggest advantage over Arkham is its size, speed, and accessibility. Arkham Horror is a MONSTER of a game. I've dedicated a LOT of time to getting Arkham Horror as concise and organized as possible, so that games can be set up and begun faster, but even with those considerations, Arkham takes, at best, 20 minutes to set up. And then Arkham takes over your entire table - truth be told, I do not have a table in my house that could hold Arkham and all its expansions. Even one expansion pushes the available table space in my home. At the place we hold our gaming group, it can still barely fit on the large table. And then, once you're done, you're in for the long haul, playing a massive game that takes a long time to teach, and a much longer time to play, with games averaging 2 hours and sometimes spiraling much longer. It's just a big friggen game.
Elder Sign you can set up in 5 (if you're slow), and fit a full game on one small table, and be done with first time players in under an hour. That advantage is HUGE. While it won't replace Arkham as my big epic game, the fact that I can sit down, set up, play, and tear down in an hour is such a big advantage that it seems likely to me that Elder Sign will be getting a lot more play t my house than Arkham Horror will, just due to size and time constraints alone!
So, in short, Elder Sign is no replacement for Arkham Horror, but it's a perfectly fine game in its own right, a lot of fun, and still dripping delightfully with the eldritch abominations we love so much. I'd highly recommend it.