Technological answer: iBeacons allow more selectivity and precision. You can be confident that a visible iBeacon is within 30ft or so, rather than 300+ft for WiFi, and with a little calibration you can measure the distance reasonably well. WiFi can tell you "the user is in [a section of] the building", while iBeacons can tell you "the user is standing in front of exhibit X".
The advantage of iBeacons, of course, is that you can do this cheaply.
Doesn't BLE have a range of some 150 feet+? That doesn't differ much from the range of 802.11g. Both of them have amplitude that you can measure, from which you could guess at distance (especially if you're near the same source multiple times).
Of course a store isn't going to set up a bunch of APs to notify you when you're near a display, but aside from channel overlap and ugliness technically they could. And outside of the walled garden that you mentioned, it would be just as suitable for the role it filled in this application.
'iBeacon' is great for very general and very localized location finding, but you're going to have a very hard time triangulating your location very precisely in say a department store.
Now I'm not a radio engineer, it may be that it was too many beacons for the area or the general wireless soup was high but it could sometimes take 20-30 seconds to see that beacon as immediate with your phone sitting smack dab on it. Sometimes 1sec. (iOS7.0 on both ipod touch 5thgen and iphone 5 devices) . Perhaps the filtering they use just needs to be tweaked a bit.