The Great Depression was global, but much of the damage was US-led, so the factors that made it a great depression, not just another footnote in economic history, are relevant worldwide. The world economy was already integrating, particularly in the areas of banking and finance, so US monetary tightening affected many European economies and currencies, causing crises in European banks and currencies worldwide. Meanwhile foreign direct investment from the US dried up, neutralizing what had been a major source of European productivity growth in that era.

Today, everyone's quit the gold standard and the forex situation is very different, blunting impacts of wild currency movements. US and European banks are not at risk of bank runs (as they are stabilized by general government policy and specific interventions), and whatever chaos we see, a ~35% contraction in the supply of USD is not on the table. If we are beset by deflation it's going to be puny in comparison.

It is worth mentioning that the Depression was also associated with major breakdowns in international trade, in part due to lots of tariffs. The bad news is we're tariff-happy again, but not as bad as Smoot-Hawley for now? The protectionist impulse bears monitoring.

And I'll finally clarify that we will still have a recession, and it might be pretty nasty. It's just not going to be Great Depression bad where we can't recover for a decade, not with just what's happened so far.