We don’t really know enough about how Respectable/Dreaded/Bizarre work yet. I think the only thing anyone’s seen that actually tests them is the option on the Connected Pet card, and the ones people have put on the Wikis only yield 1.50 Echoes on success. On the other hand, the cost to swap out is just two actions, waiting for the card, and some points in whatever connection you use.
(It also seems like Respectable’s the easiest to get, at least at low levels. Clothing from the Bazaar starts granting Respectable well before any of the other stats, and God’s Editors is one of the cheapest PoSI items. I just swapped for a Respectable pet myself, but that’s partially for out-of-game reasons.)
Zubmarine grants Bizarre, Pleasure Yacht grants Respectable. All three ships other than the Tramp Steamer unlock one new card for the Opportunity deck at Zee and one or two options on other cards. edited by Aspeon on 3/9/2012
Respectable is by far the easiest (and highest) of the new stats to raise. According to my spreadsheets (which I would name overgoat.xls if I could afford one), it is currently possible to get respectable 75% higher than the other two stats - and to get bizarre even that high requires an option that costs 100 fate and rules out a better companion. All the normal stats have different maximums with current equipment, but the new quality stats are unbalanced pretty far in favor of respectable at this time.
Of course, this lack of balance is itself balanced by the fact that there is little to nothing to do with those stats as of yet…
[color=#009900]Respectable is, and will remain, the easiest to acquire, and Bizarre the hardest. This is by design.[/color]
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[color=#009900]You’ll start seeing new uses for them come on stream soon.[/color]