[utterly stupid]

I think I have really confused myself.  When we relate two compounds in an energy diagram we say the lowest energy is the most stable.  But when we look at bond energies the higher the energy (more energy it takes to break the bond) the more stable???

[stewie griffin]

In an energy diagram, you're talking about which molecule is more stable. You're not saying which bond is more stable.
I think it makes intuitive sense that the a stronger chemical bond is means that it's harder to break, and is therefore more stable. Here you're looking at individual bonds. Higher bond strength = more stable = lower in energy.
In the energy diagram, you're looking at an entire molecule. In other words you're taking into account the strengths of each chemical bond in that molecule. The molecule that ends up being the most stable (and thus lower in overall energy) most likely has higher bond energies.