I am guessing this is mango and papaya season somewhere since my local market has quite a few varieties.
Do you have any favorite type of mango or papaya?
I ask about selecting because two of the mangos I bought were bad. They looked perfect outside. However, after a week, they still had not softened, despite being in a paper bag the last few days.
When cut open they had big black areas and were still hard. What's with that? Is there such a thing as over ripening? Did I leave them in the paper bag too long?
As far as papayas, IMO the bigger the better. However, that doesn't include those huge cooking papayas.
The smaller varieties just have two thin a flesh and have to be eaten by scooping rather than slicing into pieces. There doesn't seem to be a taste advantage.
I really haven't detected any taste difference in the mango or papaya varieties. The only difference is color of flesh in papayas with the sunrise variety having a deeper orange / red flesh which is quite attractive.
Mango varieties I've tried include Tommy Atkins (the most common), Keitt, Kent, and Hayden. Here's a link with a poster that has 143 mango varieties and their names.
Here's another link with someone's list of top 20 mangos, most of them not available in the USA due to being too fragile to ship.
Here's a mango link with some suggestions on cutting.