1.) Both episodes begin with a cultural revolution that has no precedent (the arrival of militant Protestantism versus the arrival of the counter-culture of the 1960s)
2.) Both episodes witness a fundamental reassessment of what property is. (The closing of the commons giving rise to the concept of private property, versus the modern rise of intellectual property).
3.) Both episodes see important intellectual innovation, against a background of economic stagnation (Robert Hooke, Isaac Newton, Boyle, versus the rise of modern genetics --- although, arguably, this is an area where the analogy breaks down, as nothing of the last 50 years seems to match the importance of Newton or Boyle).
4.) Both episodes see a civil rights struggle that fundamentally changes the relationship between the citizen and the state (freedom of religion being the big struggle of the 1600s, freedom from racial discrimination being the struggle of recent times).
The Really Great Stagnation ended with the Industrial Revolution. The current stagnation ends with...