Let's start by reviewing what R^2 is and what it quantifies so we can decide which model seems better.
What is R^2?
To find an appropriate a model to represent a set of data, we can perform a regression to find the curve of best fit. The relative predictive power of our model is measured by the coefficient of determination, R^2. The closer R^2 is to 1, the better the fit. You can see a comparison for some quadratic models with different R^2 values below.
R^2= 0.884
R^2= 0.943
R^2= 1
As we can see, R^2 can help us decide which model fits better. However, this can also be misleading. Sometimes, especially when we have few data points, a model can predict values that do not make sense for the related real word situation. In those cases, even if it R^2 is closer to 1 for it, another model may be a better choice.
Conclusions
Given that we have no other context for the data set and the models, and we only know that for the quartic model R^2=0.94561 and for the cubic model R^2=0.99817, the cubic model seems to show a better fit.
