Which one of these two does the hive recommend and why?

Isn't one of them single and the other one a double stack?  That should make it easy for you to narrow which one you want.  They are both well made guns.

It'll be a range gun only so capacity is really not an issue...

Having had a Les Baer and having shot a buddy's STI, I'd buy the STI if I were interested in buying a 6" 1911 type.

Have only fired my friend's STI, never even seen a Baer in person, but based on that STI, if you have the money, buy one. Great pistol.

I have the 5" Premier II.  It amazes me how tight it shoots, supposedly guaranteed 1.5" at 50 yards.

I literally just ordered a STI 2011 today too.  

Love my Les Baer TRS

Not sure why you'd want a 6" barrel, unless you're shooting .460, 10mm, etc...

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Maybe he just got done watching Terminator?

ETA: Still needs to pick up some laser sighting though.

Range gun/ longer sight radius..

I'd love either.  Baer makes a nice, accurate, reliable 1911. So does STI.  One's a single stack, traditional 1911 with slightly longer slide.  The other is a double stack with polymer, changeable grip assembly.  Really, like everything else, depends on what you want in your range gun.  I love the traditional single stack 1911.  I also love the 2011.  It gets as close to that single stack feel as possible, while giving me a shit load of ammo on tap and remaining relatively light weight.  The 2011 also gives me the option of changing grip configuration, size and texture depending on intended use.  A little more control over how the gun feels than simply changing grip panels.  Mags are expensive in the STI and not as common as standard 1911 mags but they work well.  I don't think you can go wrong either way.
 

ETA:  STI owner

I'd have to sell my remaining leg (to someone really desperate) to afford L.B.

The absolute best of luck with whichever you pick. Use it in good health!