1 : harassed, oppressed, or obsessed by —usually used in combination · guilt-ridden · debt-ridden
2 : excessively full of or supplied with —usually used in combination · slum-ridden
The first sense of ridden is negative, while the second sense simply means excessively full.
: carrying a load or burden
This word only has a single sense given, and it doesn't have the same necessarily implication of excessiveness.
Laden, when used as a compound adjective, can be associated with negative things, but it's meant more as an intensifier than a negative in its own right.
At that time, the high-priced, veteran-laden Tigers saw the writing on the wall.
There is little negative about veterans, so it just means that there are a lot of them.
Or, to make up some sentences of my own:
It was a promise-laden job.
The child had hope-laden dreams.
Unlike ridden, laden is also used in a different, and more neutral way when not combined into a compound adjective:
heavily ladened with equipment
laden a ship with emergency medical supplies
The truck was laden with gravel.