Connect speakers to my new Denon AVR-x4700H Receiver or to my Outlaw 7125 7-Channel Amp

Why don't you try both ways and see what the differences are? 

Good point 

I was hoping to learn if there were any obvious advantages of either approach before spending the money for audilo cables to pre-out from the Denon to the Outlaw amp.

my experience is that most  mass market avrs benefit from an external amp, which generally has more oomph than the internal amps in the avr. per russ69 i would compare both ways, but i'd be surprised if you didn't like the outlaw better.

I had a 7125, great amp.... that's because ATI built it.     I would use the pre outs for sure.  

Your Denon AVR  will probably run cooler if you use the pre outs.

Denons  run rather hot and heat is not gear frendly.

My 2 cents

So here’s the deal — the Outlaw amp will outperform your Denon.  Period.  But the problem is, if you care at all about music the preamp section of the Denon sucks.  It just does.  Almost all but the most expensive AVR preamp sections suck.  If you care at all about 2-channel music you need to invest in a decent stereo preamp.  Preamps make all the difference in audio.  You can seamlessly blend the stereo preamp in with your AVR and with the push of a button take the Denon out of the loop completely for stereo listening. I’m not going into the details here, but if this option might be of interest let me know and I’ll give you the details in how to make the connections.  It’s insanely simple, but do not buy a preamp until you tell me you’re interested because I need to check the connections on your Denon to make sure this can work.  My opinion is even someone with limited hearing can appreciate better sound