When I worked full time in a studio a preacher brought in a church boy band (strange but I've seen stranger). Now, these guys had a producer and he was the soundman at their church.
He suggested the label (stranger even that they were signed!) buy each one of these guys Gibson LP USA and Fender USA, Jazz Bass USA and a processor. The Fender guy ended up with a POD XT Live, other guitarist Boss GT-8 and bass the bass version of the GT-8. At that point the "producer" set each one of these guys' tones and that was it - they weren't allowed to weak or do anything. So they walked in the studio with a rigid setup and I could do was record them the way they are. I tried to raise objection as the sound was rubbish but they were told that was their sound so they just wanted it to tape.
Ironically - I could do all I wanted with the board controls and they wouldn't care. So I tried to dial in something a bit more pleasant.
I tried that during mixing even firing some of these sounds through a speaker (band wasn't there). Still - nothing got up there where I would've liked to hear it.
On the other hand with the right tweaking I can coax some usable (wouldn't say grammy) sounds out of modelers. Recently recorded a track with Boss GT-6 and a lot of guys want to copy that lead tone.
Same thing with the POD - I could mimic Vai or Satriani but nothing that I was 100% happy with.
On the other hand - active pickups guitar (in this case BCRich) into a 5150 and a sm57 and I had the right channel taken care of on the last project I recorded. A lot of people asked me how I miked that amp