I think J.W. covered it pretty well. I'll add a few things from my personal experience. I agree that tortoise is widely accepted as one of the better pick materials in terms of tone and feel. The downside is that it does wear (aside from it being illegal to harvest, manufacture etc.). As far as a woodier tone, the tortoise is great for that. Mine is .053" (about 1.3 mm) and I don't notice it flexing when I play.
I have a TPR 50 blue chip (.050" and that's about 1.25 mm). The tone of tortoise is slightly different than the BC but it is about as close as I have heard. It has rounded corners and it's a bit darker than the tortoise I have. I would characterize the tone as very woody. The rounded corners change both the feel (easier to get through the strings) and the tone (darker). I don't regret buying a blue chip and I'll buy more in the future. The downside is that they are not widely available to try out. What I'll probably do on my next order is order the ones I am interested in and return the ones that don't make the cut. I am fairly sure that if I told BC what I would be doing, they would be absolutely fine with it. They offer a 30 day exchange.
I do prefer rounded tip picks for mando. I think it matches up with the string tension better. I also like playing guitar with rounded picks, but I am more picky about pick shape with the mando.
On the thickness: I am not hung up on a given thickness, but rather I look for a certain rigidity. For me, if a pick flexes much, it gets more difficult to stay as accurate in timing. A pick with more flex gets through the strings easier and has a different, weaker tone. I play different styles and occasionally go back to a pick with a little give for a particular type of playing, but for flatpicking bluegrass, I prefer a stiff pick.