When you compare models with the same number of parameters usually is used R^2 to understand which of the models explains better the data.

But when you have a different number of parameters is normal that the models with more parameters are able to fit better the data and in the limit, if you have as many parameters as points the fit will be always 100%.

However a good model should also be parcimonious as as so it is needed to use statistics to balance the effect of added complexity with the added explanation power.

For this the most used test is the AIC.