The most significant difference in the Earth's atmosphere between these two time periods was the proportion of the atmosphere that was composed of diatomic oxygen gas (O2). This is indicated by a variety of evidence, such as fossils and chemical compositions of rocks.
Current theories suggest that the Earth's early atmosphere was composed of gases leftover from the initial cooling of the planet, gases emitted by volcanic eruptions, and deposits from comet impacts. This atmosphere was high in relative proportions of carbon dioxide, and low in oxygen. This was the atmosphere that the earliest life evolved under, eventually developing more complex metabolic reactions that utilized carbon dioxide as a fuel source, such as photosynthesis. The waste product of this reaction is oxygen.
As oxygen began to accumulate in the atmosphere, it began to react with rocks in distinguishing ways, such as by forming rust, which would not have been possible without large amounts of free oxygen. Eventually, oxygen "sinks", meaning places for oxygen to accumulate and be stored in a non-reactive manner, were depleted, leaving the oxygen to build up in the atmosphere. This is referred to as the "Great Oxygenation Event", and led to the evolution of oxygen-metabolizing reactions as the predominant form of energy in organisms.