Each of the four upgrade levels will give a bigger bonus for higher rarity levels. Items with higher rarity levels tend to have slightly better base stats, but where rarity level comes into play most is when you upgrade the item. Weapons come in 6 rarity levels with a 7th level of named legendary items. Higher the number, the longer the reload takes.
Any weapon you hover over will display their statistics to you so you can easily see how good/bad it is. The stats for a weapon can be viewed at any time by either selecting it via the weapon wheel or by clicking on it in your inventory. How much damage they do, how easily they break, etc, are all shown under these stats. These dictate the statistics of the weapon regarding how they function.
All weapons in Dead Island and Dead Island: Riptide have weapon parameters.