I've never played through a Timmy or any of the "boo-teek" overdrive pedals claiming to be ultra-transparent, but I can comment on some of my own experience with the Dano pedal, which I own:
I would call it the More-Transparent-Than-A-Tube Screamer Overdrive (MTTATSOD?

), but I would agree that it's not a
truly transparent OD (i.e. doesn't noticeably alter the EQ profile of your guitar's signal). It's still got a mid-range hump, just not as pronounced/peaky as a Tube Screamer. Which isn't to say that it doesn't sound damned good and represent a great pedal value at only $40!
As far as it sounding like a Timmy--from what I read, a guy over at freestompboxes.org analyzed the TOD circuit, and found that it was identical to the Timmy except for the ratings of two power filter caps, which aren't in the signal path anyway. Assuming that (1) he's correct, and (2) the controls can be set analogously, the two
should sound alike. If they don't....well, who knows what else might be going on?
In my own limited experience with the quest for OD transparency, BY FAR the closest I've heard to truly achieving that is an Allums "H2O Plus" modded Blues Driver BD-2. I recently installed this mod for Nelskie on a used BD-2 he'd gotten off eBay, and was so impressed with the result that I ended up buying one myself and doing the same mod on it. So for ~ $50 for a used BD-2 in good shape and another $28 for the Allums mod kit, you can have what I think is a
truly transparent overdrive--which incidentally also has a boatload of gain available at the high end of the Gain knob. It sounds just freaking unbelievable with a Strat.