Li-Ion Power Pack vs Deep Cycle 12V Battery?
...hold about the same number of AH

But there's the catch! A big one:

The mAh rating for the SLA battery is at 12 V so that equates to:

12 V * 22 Ah = 264 Whr (Watt*hour).

But for the powerbank it usually is at 3.7 V (the nominal voltage of a Li-Ion based cell), almost all powerbanks use a 3.7 V battery and a DCDC boostconverter to make the 5 V output. The manufacturers want to advertise with a large numger of mAh so they use the actual battery capacity but "forget" to tell you that that number is at 3.7 V and not 5 V.

So at 5 V you will not get 20.1 Ah but (ideal maximum) 3.7 V/5 V * 20.1 Ah = 14.9 Ah. That exclude the losses of the 3.7 V to 5 V conversion. But it gets worse, the actual energy stored is:

3.7 V * 20.1 Ah = 74.4 Whr

So the SLA battery has about 3.5 times more energy than the powerbank.

So your assumption that the same mAh rating means they also contain the same amount of energy is false!

Combined with an efficient DCDC converter to convert 12 V into 5 V my guess is that the SLA battery can easily charge a phone at least 4 times more than the power bank. In practice that 4 times might even be conservative as down conversion (12 V to 5 V) is generally more efficient than upconverting (3.7 V to 5 V).