Hydrogenolysis of benzylic C-N bond
Hydrogenolysis typically involves a metal surface ($\ce{Pd, Pt}$, etc.) and hydrogen gas. In the reaction a weak bond, that is, a bond that is either strained or a bond that can generate a stabilized radical is broken. In your examples there is no strain, but a resonance stabilized benzylic radical can be generated in one case. 

In the benzylic amine pictured on the left, the benzylic carbon can easily adopt a geometry such that when the p-orbital on the benzylic carbon is generated it is already aligned with the p-orbitals in the aromatic ring and is therefore stabilized while it develops. 

The molecule on the right is different. I built a model and as the C-N bond starts to break and the p-orbital starts to form, the developing p-orbital is twisted 45-60° away from alignment with the p-orbitals in the aromatic pi system - it is not effectively stabilized due to conformational constraints imposed by the ring system. 

Therefore this latter molecule will not undergo hydrogenolysis of the C-N bond as readily as the molecule on the left.

Here are some photos of my model:


the molecule - note the blue $\ce{N-CH3}$ nitrogen as a point of reference





conformation A - looking down the benzylic carbon - aromatic carbon bond on the left side of the photo, the N-methyl group is axial and in the foreground, the aromatic ring is planar and in the background, the $\ce{C-N}$ bond is tilted about 30° from the plane of the benzene ring, therefore the (soon to be) p-orbital is tilted about (90-30) 60° away from being aligned with the p-orbitals in the aromatic ring - poor overlap potential





conformation B - looking down the benzylic carbon - aromatic carbon bond on the left side of the photo, the N-methyl group is equatorial and in the foreground, the aromatic ring is planar and in the background, the $\ce{C-N}$ bond is tilted about 30-45° from the plane of the benzene ring, therefore the (soon to be) p-orbital is tilted at least (90-45) 45° away from being aligned with the p-orbitals in the aromatic ring - poor overlap potential