The difference between a constant growth model and a non constant growth model resides in the consideration of the firm's risk. Non-constant growth model directly considers the risk as reflected in beta in determining the required return. The constant growth model does not look at risk. It uses the market price as a reflection of the expected risk-return preference of investors in the market.
The constant growth dividend model (also known as the Gordon growth model) and non-constant growth dividend model (commonly known as Capital Asset Pricing) techniques for finding the return are theoretically the same, though in the common practice estimates from the two models do not always agree. These two methods produce different estimates because they require estimates as inputs of other quantities, such as the expected dividend growth rate and the firm's beta.
Another difference is that when the constant growth model is used to find the cost of common stock equity, it can be easily adjusted to for the flotation costs to find the cost of common stock, while the non-constant growth model provides a complex adjustment method. With the constant growth model, a firm overlooks the risk that the company may not be profitable and will have to cut its dividends that may later on reduce the stock price. The non-constant growth model sets up a firm to expect that the market may become weak and would drag the stock price with it.