How to test two polarising filters against each other?

Roger Cicala, the founder and lens guru at lensrentals.com did a series of blog articles about polarizer filters a while back.

My Not Nearly Complete, But Rather Entertaining, Circular Polarizer Filter Article

My Last Circular Polarizer Post

In them, he did some fairly controlled testing to check four characteristics of various circular polarizers at various price points:

• How well they filter the polarized light passing through them
• How much the glass in the filter affected the lens' "sharpness"
• How the polarization affected the spectral distribution of the light allowed to pass through them
• How transmissive they were of the polarized light passing through them

He found that pretty much all polarizers do the same job with regard to polarization. They all allow the light they're supposed to allow to pass and they all block the light they're not supposed to allow to pass based on the direction of the light's polarization with reference to the direction of the filter's polarization. Every filter he tested was at least 99.9% efficient in terms of polarization, which was the limit of his ability to measure with the setup he used. There was no distinction between the cheap and expensive filters.

He also found they all had virtually no effect on a lens' accuttance. There was no significant difference between the cheap and expensive filters. The quality of the glass was about the same in all of them.

He found that the "high transmission" filters all shared a similar spectral distribution and that the "non-HT" filters all shared a different similar spectral distribution from the one shared by the "HT" filters. He included charts of each filter's spectral transmission at the above linked blog entries.

He found that the greatest variation between the filters was with regard to how much light was "lost" due to reflection and absorption as it passed through the filter's glass. Filters that were supposed to be "high transmission" did, in fact, allow more light through and resulted in less loss of light than filters that were not labeled as "high transmission." He also found that the cheapest filters that were not multicoated to reduce reflections, both "high transmission" and those not labeled "high transmission" had lower transmission than their more expensive counterparts, but the cheap "HT" filters were still more transmissive than the cheap "non-HT" filters.

Here's the list of filters sorted by transmissivity when all of the light aimed at the filter was already polarized in a direction that would not have been filtered by the polarizing part of the filter:

(Unless otherwise noted, all filters were multi-coated on both external surfaces.)

Marumi EXUS* ($140) 91%
B&W HT MRC Nano* ($102) 88%
Sigma ($150) 68%
Zeiss ($180) 66%
Heliopan ($200) 58%
Tiffen Ultra Pol ($103) 55%
Hoya HRT* (not multi-coated) ($45) 53%
Tiffen CP (not multi-coated) ($35) 38%

_{* Labeled as a "high transmission" polarizer.}

Based on Roger's tests, there's not much difference between the glass itself. The difference is between the type of material used to filter polarized light and its effect of the spectral distribution of light allowed to pass, and whether the filter is multi-coated or not. A "non-HT" multi-coated filter is about as transmissive to light polarized in the same direction as the filter as a non multi-coated "HT" filter is. Multi-coated "HT" filters allow the most light to pass, and "non-HT" filters without multi-coating allow the least.

Roger also noted that higher transmissivity may or not be a desired quality in a polarizer. Many people use them in scenes illuminated by bright sunlight and, at least for some situations, the additional density of the filter is often a welcome characteristic.

Some, probably most, people don’t care about how much ND effect their circular polarizer has, and if they do they may well not want the higher transmission variety, they’d prefer a bit more light blocking. After all, if you need a circular polarizer, you probably are shooting where there is lots of bright sunlight.

After he was done, Roger noted that, as usual, no good deed goes unpunished. He hadn't really wanted to test filters but let his blog readers talk him into spending a tidy sum on the equipment he used.

After I was done, I told Aaron I had just documented that CP filters had different light transmission percentages and different color casts. And that high transmission filters had one look, and it was different than regular CP filters, which all were really similar. Because I was proud that my investment in time and money had paid off.

Aaron took the filters from me, put them on a piece of paper, took this picture with his cell phone, and said, “Yeah, you’re right.”

Since you haven't indicated, I'm going to assume that of the two filters you bought that were (hopefully¹) from the same manufacturer, one was an "HT" filter and the other was not and/or one was a more expensive multi-coated filter and the other was not.

UPDATE: Additional information from the OP:

The difference between them, as noted by the manufacturer, is the glass used (Japan Optics vs SCHOTT B 270, both have Ultra-nano coating with 16 Layers, there's no other mentioned about high transmission and no other difference in the technical information section).

Then if I were you, I'd send the high dollar one back. Based on Roger's findings with a fairly broad selection of circular polarizing filters, it's highly likely there's no real world difference between the two. Roger has found differences in the glass used in UV and clear "protective" filters. He said he also expected this to be the case with the cheaper vs. expensive polarizers, but was surprised to find that none of them demonstrated it.

He did also mention he suspected the test he used may or may not be valid when combined with a polarizer. But if the glass in question always has the polarizing material attached, then the neutralizing effect of the polarizing material in Roger's test would also have a neutralizing effect when using the polarizing filter on a camera.

_{¹ There are a LOT of counterfeit "high end" filters on the market. Some folks have suggested there are more counterfeit B+W filters in circulation than genuine B+W filters. I recently got a fake B+W XS-PRO MRC nano HTC C-Pol KSM through amazon. I returned it and bought the same filter from B&H, which was the genuine article when I received it.}