Current projections to the year 2050 reveal that fossil fuels will remain the main source of energy generation. To achieve the target limits of carbon dioxide emission, set by national and international policies, carbon capture will play a key role. Modeling and optimization of various carbon capture technologies such as pre-combustion, oxy-fuel, and post-combustion, when integrated with coal-fired power plants, have been researched extensively in literature. Research on the integration of power generation with capture technologies regarding comparisons between the different schemes in response to dynamic inputs is lacking. This work provides a comparison between a low temperature carbon capture and a chemical absorption process in response to a dynamic electricity demand and price profile and in the presence of an intermittent wind power supply. The objective in this work is to meet the overall electricity demand of residential users and the carbon capture process while the total operating cost associated with the integrated system of power generation and carbon capture is minimized. This comparison includes scenarios with and without energy storage associated with each capture technology. It is observed that in both integrated systems, with and without energy storage, the overall electricity demanded by the capture process and residential users is supplied by a combination of coal and wind power. For the case without energy storage, the total operating cost and energy demand of the low temperature carbon capture, based on a similar amount of captured carbon dioxide, are 4.3% and 20.5% less than that of chemical absorption, respectively. For the scenario with energy storage, the low temperature carbon capture requires 32.34% less energy to capture similar amounts of carbon dioxide while incurring 9.09% less overall operational cost.