Imagine you can find cheaper than brand-name of the low-ESR kind too, but that's the likely main difference between the two kinds shown. The coin type are, AFAIK, more traditional construction with high ESR, suitable for CMOS backup over some hours/days/months, and essentially no real power draw (ESR >kohms).
What ESR do you need? For a 20 second time constant I would guess the latter type, that's quite a lot of current draw to discharge a farad at, as backup capacitors go.
Tim