I have done all the above methods. Mostly before I was really interested in daylilies. My mother would get me to divide her's and we never gave any consideration to being gentle with daylilies.
Now, I do my best not to have to cut them, but I have a few there is just no other way to divide them. Plants are different and the soil they grow in makes a difference. A lot of plants can be dug and are easily divided with the gentlest of pulling to separate the fans (those are the fun to work with good ones). Others have to have all the soil washed off, then you have to use extra effort to pry the fans apart (those are the bad ones). Then there are those that you wash all the soil off off, you pry, you poke, you pull, and then you take whatever means necessary (shovel, axe, knife) to cut that mass of tangled unrelenting mass of roots (the ugly ones). Normally they are all fine and continue to grow and multiply.
That being said, there are some plants that after being divided will not miss a beat and then there are others which may miss a season or two before they start their normal growing and blooming cycle. I don't really think it has much to do with the method used to divide them.
