Pro Co Rat (1986), soldering iron, Kester 44, parts drawer, diy JTM style amp, Gibson SG.
Though I use the Rat mentioned above occasionally, I suppose I'd have to answer the OP question by saying, "I don't love it." I prefer not to have any sort of clipping at all in my tone, and I use effects sparingly in any case. This is mainly due to the nature of the JTM45 style clean tone that I get, which has the sustain and bite that I need, and has enough bass content to play the snare drum from across the room. In other words, it does not have that understated Vox bass thing. Even my strat on the bridge pickup has a heavy feel. I see that as a good thing.
TBH I've never know an overdrive sound that made me think *worship*. However I do recognise some overdrive sounds that make me want to leave the room, and the Hillsongs tone is one of them. In fairness, it's probably the style of playing rather than the actual tone that I dislike, and played differently I'd probably enjoy it a whole lot more. This isn't intended to be a rant about music particularly, other than so many worship tracks all have small variations of that sound and style that it's becoming hard to differentiate between artists, and it really detracts from the song for me.
For the little it's worth, when I play guitar - proper electric guitar, rather than synth or acoustic - then my overdrive comes from a Jekyll & Hyde (use the Hyde side for distortion - sounds nasty with Jekyll too) or Danelectro Transparent Overdrive or from my amp. Guitars are usually a Strat, Les Paul or Washburn A20V. Generally I want my overdrive to be a solid bar of tone that I can hammer and shape into a musical weapon that will make hairs stand up on necks.