Hi, Rainbird.
You've been waiting a while for any response so I thought I'd put in my 2 cents, for what it's worth.
I'm in a sub-tropical part of east Australia and mangoes are a popular backyard tree in larger yards.
It's known here, that cropping of trees in general can be very uneven, year from year. For reasons of climate, one year may be a poor result, and another year can see a bumper production.
Given that you have 2 trees performing differently but under pretty similar conditions, I'd say it's just the particular tree rather than lack of care.
If your non-performing tree was seed-grown rather than grafted, then you are at the mercy of nature. Just like flowers and flowering trees grown from seed, one may be a stunner, and one may be a "dud".
So I guess the question is, are both your trees grown from seed or grafted - if you didn't plant the 20 yr old one it may be hard to tell after all these years anyway.
The fact that it's flowering well indicates that there are the right conditions. Things that cause non-fruiting are such as... the nature of the tree (above), pollination factors (type of mango may be relevant). They are pollinated by insects as well as wind, so if one is more sheltered it may be missing out.
Sometimes if you get early flowering due to sudden warmth but then the temps drop, the tree will respond by dropping flowers to conserve it's energy.
Check for disease - anthracnose can cause flower drop.
If you get a lot of rain in early stages of flowering it can inhibit germination.
Fertilizing with manure is fine - they trees won't develop without, but you might need to treat with potassium nitrate a little before flowering is initiated to help.
Unless there is anything else you think is relevant in terms of the two trees - more or less sun, better or poorer drainage, root competition from other plants/lawn, more or less watering, then ..... you might need to talk to nursery people there.