cliffy - At the distinct risk of turning this into another tire thread with its flood of subjective comments, I'll first say that in my experience (which includes BMW's excellent two-day off-road class last year at their S. Carolina facility), you can never, ever go wrong off the asphalt with knobbies. They simply transform the bike's handling and capabilities plus increase your confidence in gravel, mud, rocks, sand, etc. versus road-oriented tires. I've learned first hand that even lightly graveled state forest dirt roads that are fine with Tourance/Anakee, etc. type tires in dry conditions are a different animal when descending a steep hill with thawing snow and/or light mud.
The first time I ever really took my GSA off-road was to an OHV road with rocks, mud and water crossings. I stupidly did the loop with Anakees instead of knobbies, and four bike drops later (with an equal number of solo pick-ups, of course
) I was exhausted but made it back out to the highway for the 100 mile ride home (see pic below). I might be slow, but I do learn from experience and won't make that mistake again!
The Heidenau K60s worked well for me both on and off road (as good for me off road as TKC-80s, but a better rider I'm sure can tell a difference). On road, the best thing about the K60s was their great mileage. Didn't like them at all on wet or dry tar snakes (definitely worse than Tourances, in my experience different tires definitely handle tar differently) and the rear slipped a bit once or twice on wet road cornering (not unexpected with knobbies), but there was always something about their dry road handling that just kept me from being fully confident and pushing in corners like on TKCs. Might be attributable to the K60's squarish rear tire profile, and the front K60 lightened the steering like no other tire I've ever used (felt too vague to me). Many have said the K60s are really tough to mount but mine spooned right on using my tire irons on a cool day. Removing them was an altogether different matter though, some of the toughest tires I've ever done. TKC-80s just fall on and off the rim by comparison.
All tires present some type of compromise, and in spite of me thinking a few times about another pair of K60s I don't think I'm going to go that route again. IMHO, the only thing the K60s have over TKCs is mileage (for me, at least double the miles) but my confidence and satisfaction with handling is worth more than any cost savings that brings. While Tourances are my all-around favorite road-oriented tire, the only reason I remounted them was for my June trip out west (all highway except taking the back way into Badlands Nat'l Park on dirt roads). The rougher ride, noise and lower mileage of knobbies just made no sense for that trip, and as soon as they're used up another pair of knobbies will be going on.
Based solely on my experiences with these tires, I hope this helps answer your question.