This is just my own opinion in comparing these 2 subwoofers in my car. I can't post pics yet as my post count is too low but I can add some later on for comparison.
I already owned the Alpine R-W12D4 which was a brand new warranty replacement for my SWR-12D4 which developed a failed triple joint. The old SWR-12D4 had the black dustcap whereas the new R-W12D4 had the grey one which I thought looked a little nicer.
I found the JBL for sale brand new and wanted to try it as I heard great things about it. I planned to sell off whichever woofer I liked less after testing.
Initial comparisons were made with each sub in their own enclosures which I custom built to be as close to manufacturer specs as possible. Both subs were ran ported. They each ran off the 500 watt sub channel from an Alpine PDX-V9 with the gain set accordingly.
As the Alpine was my first sub I had nothing to compare it to as a reference, but after swapping it out for the JBL some very big differences became apparent.
I found that the JBL subwoofer was much punchier. To me, the Alpine delivers a loud droning bass versus the W12 GTI which comes across as very punchy and "tight" sounding. One way I could describe this is that with the JBL sub at loud volume it feels like someone is punching the back of the drivers seat and the bass punches are very distinct and well separated. The Alpine sub in comparison was still loud but in more of a droning manner and not nearly as impactful.
With the Alpine the higher bass notes from the sub lost a lot of volume requiring the LPF to be set quite low at around 60 hz to avoid this from happening. I found that the problem with setting it this low at higher volumes is that the front door mid bass speakers would start to distort. The Alpine R is loud on low bass only and in songs where the frequencies shift upwards it seems as though it loses a lot of impact if the low pass filter is set high enough to allow the sub to play these frequencies. I only really noticed this issue after switching over to the JBL W12 GTI - that sub really exposed what I would now consider to be a weakness of the Alpine. The W12 GTI really is a well balanced subwoofer.
With the JBL sub I've been able to set the lpf up at 120hz 18db/octave and it sounds great. In the same type of music that would lose a lot of impact with the Alpine at the upper bass frequencies the JBL sub just keeps going with no apparent reduction in volume and impact. At these frequencies the Alpine seemed to fall flat on its face and become very easy to localize.
I ended up parting ways with my Alpine R-W12D4. It was a decent sub but for me the JBL W12 GTI easily won out in this bake-off.