We will be in the area in mid-June 2005, with interest in hiking, sightseeing, and relaxing in a 3 or 4-star property. What are the differences between these towns? I'd be grateful to learn people's preferences between these two, and reasons for same. Thanks!

You could debate till the Swiss cows come home about these two gems, both offering some of the most stupendous views in the Alps. But one factor is that Murren is more isolated-reachable only via a funicular then mountain train or a cable car from the valley. Wengen on the other hand is much easier to reach from Interlaken or Grindelwald, with quicker train connections. Both towns are car-less but you can drive to Wengen, don't think you can to Murren-no roads go up the cliff it's perched on. You leave your car in Lauterbrunnen in the valley below. Wengen, lower altitude, may also be warmer. Some will argue that Wengen has better more panoramic views - 360 degrees of Alpine glory where Murren's view are mainly to the east from its eagle-nest perch on the edge of the Lauterbrunnen Gorge. A Swiss Pass covers travel to both. A classic jaunt is to take a Swiss postal bus from Lauterbrunnen to Stechelberg, at the end of the valley and then take a dramatic aerial cable car straight up the cliff to Gimmelwald, a lost-in-time farming hamlet, and then a cable car (or a short but steep hike) up to Murren, then take one of the most awesomely scenic mountain trains along the cliff's edge to the funicular that plunges back down to Lauterbrunnen. (All covered by Swiss Pass, though if just in this area, investigate the Regional or Jungfraubahn Passes so locally). One problem with Murren is that I've seen long lines for the funicular to get down to Lauterbrunnen, though this would be seasonal.
Both are gems!

Thanks, PalQ, that's very helpful!

You don't drive to Wengen. You park your car at the train station in Lauterbrunnen and take the train up to Wengen (about 15 min).

If you are looking for pure solitude, Murren is your better choice (tho' I don't know how perceful it will be in June - we were there in early October). Wengen, on the other hand, has a small Swiss village feel yet has numerous shops, restaurants, etc. as well as the cog railway station from which you can reach the Jungfrau and other points along the way. We went to Murren for an afternoon and really loved it (easy trip up from Lauterbrunnen); but stayed for four days and nights in Wengen and it was spectacular. PalQ is correct, the vistas of the Alps are better from Wengen than from Murren. We stayed at the Hotel Regina, had a 1/2-board plan and thoroughly enjoyed the family atmosphere and hosptality, and the gourmet evening meals. Would definitely book there again on a return trip.

Asking for differences in those two is like trying to split a quark.
Both have outstanding attributes.
I visit both of them when I am in the area.

Thanks to all for advice, especially the physicist perspective