There can be many differences, but this does not mean that one is necessarily better than the other.
A book written soon after an incident is more likely to be a primary source. It is more likely to be written by someone who was directly involved and to be written based on the author's own observations. This can be a good thing because it records the way people thought about and perceived the incident as it happened and soon after it happened.
However, this can be a weakness as well as a strength. A book written long after the incident has happened has a better chance of understanding the true importance (or lack thereof) of an incident. A book that is written right after an even might inflate the event's importance because it is written so close in time to the incident.
Books written soon after an incident are more likely to accurately capture the spirit of the time in which the incident occured. However, they are less likely to be good indicators of the ultimate significance of the event in history.