what's going on with specs?

Pay attention to what many do not publish.
Current & Capacitance?  Sometimes you have to call. Not sure what you mean by strong but if you want resiliance during demanding transients then capacitance is your friend. Also, the actual details of the power supply(VA). Numbers matter, but only a little bit. Watts rarely are the tale of the tape. 

Now you've done it miller. Equated being an audiophile with religion. and that's anathema. Get it? Ha ah. No doubt that say the JC5, BHK 250, Bryston 4BCubed will all sound great. All priced near each other and listening to them at different stores will not help. This may be wrong but it seems to me the more expensive amps $20,000 and up all seem to double power from 8 to 4 ohms. Other measurements could go either way like distortion on less expensive amps can show better than more expensive ones so i agree specs are not everything. But that doesn't mean they mean nothing right? There is some reason a Boulder amp is going to sound better than a Sony receiver and it must show in some measurements. Those are the three I'm looking at and was wondering if anyone had any experience with them or should flip a coin. Oh and the Anthem STR is another contender in that price range. Any knowledge would be appreciated. 

It looks like the BHK 250 has more distortion 20 - 20 k than the Parasound whether it's audible  I have no idea. Of the 4 you mention paired with the Elac I doubt you could hear a difference, the BHK perhaps since it has tubes tossed in probably why it has more distortion. 

Measurebator, a classic from Chuck I won’t soon forget

Full disclosure, much as I would love it to have been mine I must credit uber photography guru Ken Rockwell for coming (ahem) up with measurebator.   

But that doesn't mean they mean nothing right? There is some reason a Boulder amp is going to sound better than a Sony receiver and it must show in some measurements. Those are the three I'm looking at and was wondering if anyone had any experience with them or should flip a coin. 

No, they really do mean nothing. Just because I'm good and funny doesn't mean I'm also not good and serious. You really do need to figure out what kind of audiophile you are, and what you want. Right now it seems you are a measurebator and if so fine you will find the web chock full of specs you can download and get off on. If you want music though they trust me, you can very safely totally ignore all specs and do just fine.   

Seriously. Ignore all specs. Do just fine. Pay attention to listener evaluations. IF you want to listen to music. If you want to measurebate, flip a coin. Or throw a dart. Who cares? Either way you will have some meaningless measurements to get off on.