I don't know about other brands, but the YLI .003 monofilament nylon thread that Harriet Hargrave recommends seems not to differ much, if at all, from regular thread in terms of longevity, etc. It is similar in thickness to fine baby hair and breaks about the same as regular thread.
The one warning about it that seems to have legitimacy is to not use it in baby quilts because of the risk of it winding around a baby's toe and cutting off circulation. The problem is that its transparency makes it much more difficult for an adult to see than regular thread, so there really is a risk that it will stay wound around a baby's toe or finger too long.
There are other types and sizes of "invisible" thread on the market; I'm not sure how all of them act in the long run. I know Superior Threads recommend a polyester thread, but I haven't read up on it yet.
I like the .003 nylon monofilament for certain applications such as invisible machine applique (although I want now to experiment with fine silk thread for that) and once in awhile for quilting. I wouldn't use it on every quilt, though. There are a *lot* more decorative threads available for quilting purposes these days than there were when HH first tried nylon monofilament.
In my opinion, machine quilting never really looks like hand quilting anyway. HH's method comes closer than any others I have seen, provided you also use a batting that shrinks enough to camouflage the stitching and you stand back a little from the quilt.