Resonant frequency

^ This.

Also, in certain cases, if you EQ down the ported design into matching frequency response of the closed design or vice versa, it appears that GD and other parameters become fairly close to "absolutely same". Yes it certainly is different design with different underlying function, but making it into evil ugly design that sounds bad, I don´t think so. It´s just in the application.

For the original question - if you tune your system below Fs, nothing much happens. You get your mind poisoned with small signal behavior simulations and evaluations of others. That´s not how it works.
In large signal domain, the driver doesn´t have problem to move its Fs 10Hz down when stretched in larger excursions, and so suddenly your system is tuned above speaker Fs anyways.
Various things are happening, but these are linear, these don´t break very steeply as you move in frequency. For certain price, you can sacrifice one thing for another adequately. I have high suspicion that the driver itself makes more change for these reasons, than fairly small alterations of the enclosure.
I use critically damped 18" in ported design and kicks the shiz out of me. No long slow bass, more so if I cut it higher in order to mimic the closed box response.
 
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It depends on the programme material and the system in question, but it's technically possible to create a very low-tuned (as in 16Hz or < ) EBS vented box with similar GD over most of its passband to a critically damped sealed, but with a final 'kick' of extra output around Fb in the infrasonic range. Not a bad compromise to have, but it needs the drivers & system to be able to do it. Still, the potential is available, even if it's not viable for many conditions. Assuming you don't regularly play material with content below, say, open E double bass [roughly 42Hz] you can get away with something tuned a bit [a bit 😉 ] higher for similar benefits if you're after a well-damed system & you're particularly suseptible to overhang.

Frankly, I don't think all that many are -or in a good proportion of cases, not as much as they might think, because far too many vented box systems either aren't designed with a particularly good / 'practical' alignment, or haven't been optimised for a given situation and what they're in fact hearing are the consequences of this rather than a fundamental issue with the box type itself. Not to say they don't exist, but it can be exaggerated. This can be where Dave's resistive-vent boxes can come in, or more prosaically, 'just' a well designed vented, be it Helmholtz or QW based, with a decently damped system rolloff and not excessively undersized to prevent excessive overhang. And if you want to critically damp it via the old click test for the situation (not a difficult or time consuming task, especially for something that reaps dividends) -so much the better of course... 😉

Speaking of which -the click test isn't the sole preserve of conventional vented boxes: you can use it for any vented type, be it a horn, TL variation, or even sealed & resistively vented (not-actually-'aperiodic') boxes for that matter. A 1.5v dry cell, toggle switch & a few bits of bell-wire doth not a heavy investment make & you can home in on optimal damping for a given enclosure faster that way than pretty much anything else. The pioneers knew of what they spoke...
 
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