The Subha O Sham K Azkar carry great meanings and provide a formidable source of protection. A person should try to recite the morning supplications after Fajr, and the evening supplications after Asr. This also makes perfect sense in that you complete the morning supplications just before morning starts (sunrise), and the evening supplications just before evening starts (sunset) so that you are fully protected at all times.
Some benefits of constantly reciting the morning and evening supplications:
Provide you with peace and tranquillity
Allow you to get closer to Allah
Give you strength to carry out your daily activities
Provide you with success and good health from Allah as you begin your day and end it by relying on Allah in all your affairs