Sufrimiento vs. padecimiento

The Spanish words 'sufrimiento' and 'padecimiento' both could be translated as 'suffering' or 'sufferance', but there are subtle differences in their connotations and typical contexts of usage.

Sufrimiento

'Sufrimiento' refers to the overall sensation of pain, distress, or hardship. This can be physical or mental/emotional. It often implies an enduring state of suffering rather than a temporary condition.
No puedo soportar más sufrimiento.
(I cannot endure anymore suffering.)
Este es un camino lleno de sufrimiento.
(This is a road full of suffering.)
El sufrimiento mental puede ser tan duro como el físico.
(Mental suffering can be as harsh as physical one.)

Padecimiento

'Padecimiento' also means suffering, but is more commonly used in medical contexts to refer to diseases or ailments. It implies a more temporary state of suffering that has a specific cause such as an illness (even chronic).
El médico está tratando mi padecimiento coronary.
(The doctor is treating my coronary ailment.)
Este padecimiento es común en personas de edad avanzada.
(This ailment is common in elder people.)
No he conocido a nadie con ese padecimiento antes.
(I've never met anyone with that ailment before.)

Summary

'Sufrimiento' and 'padecimiento', though similar in broad meaning, tend to be used in different contexts. While 'sufrimiento' suggests a sustained state of distress or hardship, either physical or emotional, 'padecimiento' refers to easier quantifiable suffering often associated with physical illnesses or medical conditions.