The structural differences between Bedrocks and standard Bailey bench planes are available from the link to Patrick Leach's site given above. I don't think it's right to say that he thinks the Bedrock's are *all* hype, just that the magnitude of the hype is more than the actual improved functionality (his opinion, though an informed one).
Among user's, this issue stirs up a lot of controversy and opinion. Everyone has their favorite plane, and probably spend more time honing and fussing over it than any other. That tends to increase the performance gap over others. For many people, their favorite is a Bedrock, but that still could be just emotional (or not; I don't think that's all, but don't have more than my opinion to prove otherwise). Often, a favorite plane is one that worked well without fussing, irrespective of design.
All that said, I think it's worth noting that all (or all I know about) contemporary makers of high quality planes use frog or iron bedding designs that involve large machined mating surfaces to reduce chatter. Heck, even the only plane Patrick Leach chose to manufacture was a Bedrock design, though that might have been more for novelty than function. Maybe everyone's still riding historical hype, but I'm not inclined to think all the extra effort spent in manufacture has no practical significance.
A tricked out Bailey (i.e., aftermarket blade, lapped, fettled) will outperform a stock vintage Bedrock. So given the relative price of Bedrocks, you can probably get a good plane for less by that route (in USD, $20 for the plane, $35 for a high performance blade, a couple hours time versus $100+ for a run-of-the-mill Bedrock). However, a Bedrock that's fully tuned will (IMHO) perform even better (and cost more too).
FWIW,
Dave