So, we all know that incandescent filament type black light works very poorly because a filament does not produce much UV. I've believed that a CFL black light is every bit as good as long and cumbersome regular fluorescent black light. Actually I thought the CFL version is more intense, because you have a 13W lamp in such a small area.

CFL black light lights up a lot brighter, but I expected that as the power density is higher. When I actually tested the two out side by side, the CFL black light was abysmal. The picture shows CFL 13W vs F20T12 lit up side by side. The CFL looks that much brighter with my eyes too.

The set of fluorescence corresponds to each lamp. These pictures were taken with a yellow filter over the camera lens. CFL black light would not cause dust to glow and you can see the glow on a piece of fluorescent orange fiber is very little compared to real black light.

Any idea why?

Being cheap and not evaluating the impact of all product modifications.
For a black light you need two things: Emit the long wave UV and block all visible (because you need usually quite high UV power to have lot of things glowing, as those things are not that efficient "phosphors").

The safety requirements then ask for blocking the short wave UV as well.

Normally the low pressure Hg discharge does emit only the short wave lines, so you need a phosphor to convert it into the long wave UV you need. As this is made only specifically for this, it needs special production run just for these black lights. In a high volume manufacture environment of cheap CFL making quite problematic. So some cheepeese makers just skip that, sufficing with the tiny amount of UV each lamp normally radiates.

Then you have to let that UV pass out of the bulb. Well, exactly opposite than with normal CFL production.
Here, what could easily happen: A CFL line is set up and running, while few times the phosphor mix is replaced by the black light type to make a batch of black lights The rest of the manufacturing is then kept the same. But this happen only rarely, the majority is the normal light products. The production works well.
But then someone come with an improvement: Use other glass, so the normal lights emit less of the UV. For the normal production an improvement, but then when the "black light" batch is being produced, the meed to replace the glass material for the older one is overlooked. So the result is a "black light" using a glass, that block the UV, well not that useful...

And the last thing is the filter: Using Wood glass (the best filter known) is out of game now (it is expensive and it does contain lead, so not allowed anymore). Then there are many lacquer filters, with greatly varying quality. Of course, the better ones, so with blocking more of the visible and passing more of the desired UV, are more expensive.
With poor filter, the abundance of the normal light will then just blow off the weak phosphor glow of the illuminated things (the desired effect), so the UV output then appear as too weak.

The linear tube manufacturing have less of the glass processing steps, so it is logistically easier on the manufacturing floor to really use special dedicated glass tubes for each product, together with the phosphor mix.
And these tubes usually sale for quite a lot of money, so there is plenty of budget for all the customization to be done.