I don't think the card type (store, CU, major bank card) matters nearly as much as almost all of the other data surrounding the account(s).
Someone could have a major bank card that is barely used. Maybe it's a $10k Amex card that has a "high balance" of $100 for example and a current balance of $0. Compare that to someone with a $30k Lowe's card with a "high balance" of $10k from a bunch of home projects with a current balance of (say) $200 and that Lowe's account tells a potential lender a heck of a lot more about the cardholders ability to pay down a large balance. That's just one example of course.
I think the "answer" here though is that it's very lender-specific. There's no blanket statement or "rule" that's going to cover all examples/situations... like "all" lenders view store cards [relative to bank cards] a certain way, etc.
Bear in mind too that one's total credit limit can matter a lot to a CC issuer (though not to all of them -- as other folks here have stressed there is wide variability in what criteria affect their own internal policies).
In Dec 2018 I had FICO 8 scores in the 840s, no store cards, 12 major credit cards, the highest of which had a CL of 30k.
In Jan 2019 Cap One approved me for a 30k card but NFCU (three days ago) only approved me for a 10k card.
With the Cap One card, my total credit limit was about twice my gross income. Maybe NFCU would have given me a higher starting limit if my total CL had been lower?
Thanks to all that replied! All answers were very helpful and gave me some additional insight!