I prefer #1, the circular polarizer. The contrast is better, and there are other differences. In particular, the blacks are blacker and more numerous. Did you remember to rotate the polarizers to exactly the same position? You didn't mention that. Is the linear filter coated? Here's a histogram.

Histograms of combined RGB values. Circular (left) and linear (right). Notice the pronounced differences in peak heights, with slightly darker and much more numerous grays in #1.
From the midtone peak positions, the exposures are surprisingly close, but #2 appears to have slightly more exposure overall than #1. You used the same camera settings for both, but different filters transmit different amounts of light.
There is a lot of clipping in the blue layer. That is due either to overexposure or to printing too light from the raw file. That shifts the color of the sky toward green, especially near the horizon of #2.

Histograms of the blue layer. Circular (left); linear (right)
Compared to the circular polarizer, the linear polarizer is strongly biased toward blue, and slightly biased toward green. Here are the histograms from an area of concrete.

Histograms of an unshadowed part of the concrete. Circular (left) and linear (right). From top to bottom: R, G, B. Notice the shifts in modes, which signals a bias toward G and especially B.
There are several possible reasons for the differences.
1. In the Lens Rentals article (see post above) there is a picture of some filters, and you can easily see the differences in transmission
and color. Different coatings could also have an effect.
2. Are you sure the linear polarizer is coated? This could artificially lighten the shadows and reduce the contrast.
3. As mentioned previously, you may not have the filters at exactly the same rotation.
4. As mentioned previously, the exposures are slightly different, probably because of a difference in transmission.
5. The sky is overexposed or printed too light.
As far as I know, none of these effects has anything to do with whether the filter is circular, so
please do not tell people that a linear filter has more "pop", because nothing you have done is representative of any filters but yours.