How does altering the fat-to-flour ratio affect the pastry?
Flour (+ water, either directly or from other ingredients such as egg white) gives the pastry structure. As you knead the flour, the gluten network develops and results in elasticity. When cooked, water evaporates from the dough leaving a rigid gluten skeleton. 

Fat does not mix with water and thus stay in blobs in between the gluten network. This weakens the gluten structure, making the pastry crumble.

For this reason, you often see in recipes for shortcrust to avoid overmixing the fat. Buttery biscuits such as shortbread crumble more than crackers, which have more water. The same rationale applies to puff pastry. The thin fat layers are impermeable, so water steam gets trapped and exercise pressure upwards, lifting the pastry up.

Quoting @GdD in the comments, the punchline is:

more fat = crumblier, less fat has more structure.