There IS a difference IF any of the footage was shot with IMAX cameras (as was the case with the last two Nolan Batman films). IMAX film has much greater resolution and it's clearly visible, even on the Blu-ray--more so on the IMAX screen. However, in cases where the film wasn't shot in IMAX at all, the difference in quality can vary from almost nothing to significant. Depends on the conversion process. The sound, however, is almost certainly going to be better in an IMAX cinema.
This is exactly right. Any footage (or movie) not shot with an IMAX camera gets digitally processed and "upscaled" (they call it their DMR technology) to look acceptable on such a big screen.
To me it's hardly worth the premium price for a movie that has no genuine IMAX footage in it, unless all the other theaters around you have really poor sound and/or image quality, which is where IMAX theaters always deliver.
For those that say they don't think IMAX offers much a difference, it is possible you've been to what many refer to as a "lieMAX" theater and not one of the proper more "old school" IMAX venues, many of which are shaped more like a dome, or are at least generally very large, much larger than what you'd see in a conventional multiplex.
Most "lieMAX" theaters are basically just converted standard movie theaters, where they sacrifice a row of seating to put in a larger screen, upgrade the sound, often upgrade the chairs, and put in a bit higher-end digital projector. These theaters are more like the premium upgraded theater experiences such as Cinemark XD and Regal RPX here in the US than a real IMAX theater.