Most stretch wraps have a lot of stretch, which makes them great as a first wrap and for very young babies, but IME they start to become less comfortable and need more adjustment with older babies/toddlers -- the BaliBaby Stretch does not have the same type of stretch... it can be used for toddlers and preschoolers (up to 35-40 lbs) in pretty much all carries that a woven/gauze wrap can be used for (I confess I never tried torso carries, but I bet they can be done with a BBS - can't really say for sure though!!). I have a Moby and two BaliBaby Stretch (and two nonstretchy wraps) and the BBS is my go to carrier for my 2 and 3 yo.
I've never tried a Hug A Bub, but from what I've seen, it seems fairly similar to a Moby in stretch-factor -- so I'd say, GREAT for a young baby, but probably will begin to need more and more adjustment to compensate for stretching out with longer wearing at around 15-20 lbs.
If it is mostly for your little baby, then one of the stretchier wraps you asked about might be ideal. For your toddler I'd go with a woven/gauze or a BaliBaby Stretch - and of course either of those is fine for a newborn too, so they would give you the ability to wear newborn through toddlerhood with one wrap. Nursing in a woven generally means loosening a bit (unless you wrap baby on in a cradle/nursing hold in the first place, which I never do) but is very doable in woven or stretch wrap!