Are these statements about change in enthalpy contradictory?
They are basically same statements. We can use Hess law to elaborate these two statements. For example, we can use the following reaction,
                                 CH4=C+2H2
Here, Delta reaction = Enthalpy of CH4 - Enthalpy of C + 2(Enthalpy of H2).......(1)
We can break the reaction events as,
1) Breaking of 4 C-H bonds 
2) Formation of 2 H-H bonds
So, delta H = Energy required to break 4 C-H bonds + Energy required to forming two H-H bonds.......(2)
Now we always take the reactor to be the system and that's why heat input to the reactor is positive and heat going out of the reactor is negative. In the formation of bonds, the energy are released, so the formation energy of H-H is negative with respect to our thermodynamic system.From 2
So,  delta H = Energy required to break 4 C-H bonds - Energy released in the formation of two H-H bonds.......(3)
Now, energy required to break 4 C-H bond= Energy of C + Enrgy of 4 H - energy of CH4
                                        =-Energy of reactants...(4)
Similarly,  energy required to form 2 H-H bond= Energy of 2 H2 - energy of 4 H
                                              =Energy of products (As C is in reference state).........(5)
Adding 4 and 5 yields, equation (1), which proves that both statements are same.