Comparing linear statistical models

[Motion]

I have a task in which there are two statistical models and I am asked to choose the better one and argument my decision. The problem is according to some of the data one of them is the better, and according to others - not.

Model1
Mean dependent var 51113,21 S.D. dependent var 7289,625
Sum squared resid 41370104 S.E. of regression 1029,938
R-squared 0,981464 Adjusted R-squared 0,980038
F(3, 39) 688,3203 P-value(F) 8,48e-34
Log-likelihood -357,2170 Akaike criterion 722,4341
Schwarz criterion 729,4789 Hannan-Quinn 725,0320
rho 0,744713 Durbin-Watson 0,640690


Model 2

Mean dependent var 51315,50 S.D. dependent var 7254,802
Sum squared resid 42176786 S.E. of regression 1053,525
R-squared 0,980455 Adjusted R-squared 0,978912
F(3, 38) 635,4062 P-value(F) 1,68e-32
Log-likelihood -349,8093 Akaike criterion 707,6187
Schwarz criterion 714,5694 Hannan-Quinn 710,1664
rho 0,783398 Durbin-Watson 0,551705

So the R and Fitted R values are somewhat higher in the first model, but the information criterions ( AK, Schwarz and HQ) show less reliability in the 1st rather than the 2nd, so this is where I am getting a little bit confused and unsure. Tests are made using gretl

All kinds of help or guidances are more than welcome :)

[Link]

Looking at your dependent variable statistics, it looks like you're using different ones for each model. Is this correct? Normally, comparing different models is reserved for when you are modelling the same dependent variable.

[Dason]

So the models used different data? You really shouldn't compare anything that uses the likelihood to compare models then.

[Motion]

Well not exactly.
The first one is Consumption = f(DY, IR, RPI)

And the 2nd one uses again the same DY and RPI values, but this time with the differentiated values of RPI

Consumption = f(DY, IR, ΔRPI)