The second equation gives the delta H for the REACTION as it is written from reactants producing products. The numbers one uses comes from tables which have been prepared from experimentally measured HEATS OF FORMATION (or calculated from different heats of formation using Hess' Law). They are called standard heats of formation and labeled delta Hof and they are at 25 degrees C. They are quite accurate. The values from the first equation CAN be used for the same thing; however, whereas the delta H formation values have a number for each molecule, the bond values for the first equation are averages for C-C bonds, C-H bonds, C-F bonds, etc., from ALL kinds of atoms/molecules. Thus, the first equation gives a quick way of calculating if one doesn't have the formation values handy but they only give approximate values since they are formed from averages.
That helps. But I still don't understand why we subtract the reactants from the products in one case and when using bonds we subtract the products from the reactants.
The easiest answer is that "that's the nature of the beast."
The bottom line is that when reactions take place, we usually go from a higher energy state to a lower energy state. Subtracting as we do gives the correct sign for our "defined" delta H (negative for exothermic reactions and positive for endothermic reactions). We define exothermic and endothermic together with what we define a + delta H and a - delta H to mean.
Thanks so much!