Generally speaking, when one country's currency is worth more than that of another, it does not necessarily indicate a stronger economy.
For example, Japan's economy is regarded as one of the world's strongest, and yet a single Japanese yen exchanges for considerably less than US$1. On the other hand, Cyprus' economy is considerably smaller than the U.S. economy, but Cyprus' euro currency exchanges for more than the U.S. dollar.
The fact is that looking at a currency's worth relative to that of another currency at a static point in time is meaningless; the best way to judge a currency's worth through monitoring in relation to other currencies over time. Supply and demand, inflation and other economic factors will cause changes to a currency's relative worth, and it is these changes that ultimately indicate value.
For instance, let's say that at the beginning of the year, the U.S. dollar was worth 1.75 XYZ dollars (a fictitious currency), and six months later, the U.S. dollar is worth 2.00 XYZ dollars. In this case, the U.S. dollar increased in value over the XYZ dollar by around 14%. This change could be due to XYZ having higher inflation, or to just an overall lower demand for the XYZ dollar.
A currency's purchasing power can also be used as an indicator of the relative worth of currencies. For example, if US$1 can be exchanged for XYZ $1, it would appear that the XYZ dollar is worth as much as the U.S. dollar. However, if the purchasing power of XYZ$1 is equal to only US $0.50, then you can conclude that the U.S. dollar is worth more than the XYZ dollar, because a single U.S. dollar can be used to buy more goods than a single XYZ dollar.