I had a TIM and now have a KOT but an earlier version. The KOT has more midrange. You will notice that the TIM (timmy most likely the same) leaves a touch of mids out. The TIM I had seemed to add some hi end sparkle to the notes where the KOT does not (more neutral). Both pedals are great but they are not the same.
The boost side of the KOT is more like an RC Booster that has the gain set around 2. The gain side of the KOT adds more hair to the notes but is never full out saturation. I think with the KOT V4 you can cascade the channels, I wish I had this option on mine as I can only use one side or the other but not both.
Overall I would think the KOT would be more useful but lots of people like the Timmy pedal. If you amp lacks mids I wouldn' suggest the TIM or Timmy pedals, but this is my opinion.
If you lower the low and high ( clockwise ) knobs on the timmy, you can get plenty of mids, but it will be an overall flatter mix compared to say the notched sound/mid-hump in a ts-9 type pedal. The kot is a couple notchs above the basic ts-9 though. The Timmy is a much more stackable and useable pedal.. for more styles of music.. than the kot, imho. The kot nails that organic fender sound.. and is like comparing 400 grit sandpaper, where the timmy is more transparent and is more like a rougher 100 grit. Make any sense?
I've had both pedals, and despite the KOT having 2 channels, the Timmy is a more versatile pedal. The KOT has the classic OD mid-boost, more like a tubescreamer, which is fine and makes the gain sound good. But I like the fact that the Timmy can sound transparent at low gain levels with the EQ knobs cranked but then has a great midrange boost when you roll the EQ knobs down.
It took me a long time to appreciate the EQ knobs on the Timmy, but it's amazing that bass and treble knobs can also have such a strong affect on the midrange. Paul C. has made one of the great OD circuits.
The Timmy is the most versatile pedal I've ever owned. I mainly use it for alt country/Tom Petty type tones, but it stacks really well with my other pedals too. It's like the swiss army knife of pedals.
They're both great pedals. The Timmy has a lot less mids (not at all like your traditional tubescreamer), and also has a lot more gain on tap. The KOT feels a lot tighter than the Tim though, with a bit more definition at low gain - I assume this is due to the lack of a mid boost, or maybe that's just how the gain works.
The Timmy is much more versatile, but I love how the KOT makes my tone shimmer. I'd recommend hearing them both before making a decision.