I have two items shown below. Tooltip on new bow shows that I'd have 43.3 damage decrease, however actually equipping it boosts damage on character sheet from 1639.70 to 2094.44.
After thinking a little, I figured out this is due to DH's "Archery" +15% bow bonus not being taken in account on tooltips.
What parameters exactly are taken in account in those "stat changes if equipped" tooltips and what are ignored?
(I've had additional question what is better in the end, but it is already covered in: Is there a non-DPS reason to favour a crossbow/hand crossbow/bow?, as mentioned by Alok).