The major similarity between these two time periods is that both were periods of Westernization and economic progress for Japan. In the Meiji Era, Japan first opened itself to the West. This led to industrialization and also to many cultural changes that made Japan more like the West. The same type of thing happened in the time after WWII. This was the time of the Japanese economic miracle. It was also the time when the Japanese government was being converted (under American direction) to a more Western and democratic system. In both eras, then, there was a significant move to Westernize and to modernize the economy.
The major difference between the two is that the Meiji Era was accompanied by a growth in Japanese military power and status in the world where the time after WWII saw the opposite trend. After WWII, Japan essentially disappeared as a geopolitical factor with the strict limitations on Japanese military and the move toward pacifism brought on by the catastrophe of WWII. We should also note that the Meiji Era reforms were done in the name of restoring the Emperor to power while the Showa Era reforms explicitly removed the Emperor from that position.