I'm aware of two theories. The first is geography. Great Britain is literally an island, while Spain and France might as well be islands because they're peninsulas with very mountainous borders (Pyrenees and Alps). You could also say France is like an island for the same reason. So Western Europe has a lot of geography that makes invasions, not impossible, but difficult. On the other hand, Eastern Europe is completely flat. It's also the westernmost edge of the Eurasian Steppe, which, historically, has served as a kind of highway for invaders.
Another theory (and I'm pretty sure I read this in Why Nations Fail by James Robinson and Daron Acemoglu) is that the Black Death hit Western Europe much harder than Eastern Europe. This created labor shortages and created power-sharing institutions that handicapped the monarchs. Nothing similar happened in Eastern Europe.
What's the quality of these two theories? Are there any others?
I would question the premise that Western Europe has "historically been more stable than Eastern Europe," at least in such a broad formulation. In the early modern period we have tremendous conflicts like the Thirty Years' War, the War of the Spanish Succession, the War of the Austrian Succession, the Seven Years' War, etc. Western Europe is also, of course, the epicenter of the French Revolution, and scene to a variety of revolutions thereafter. This doesn't match most people's definitions of stable.
It would be helpful for potential answers to your question to specify: