If a power bank of 10000mah and a phone of same rating is in use for an extended period. Say d power bank is used to power a phone with weak battery.

Which of the two will die faster and why

From experience d power bank seem to die out faster Even when it's twice d power rating of d phone n I dnt kw why

It's because power banks charge phones inefficiently, part of the power is lost in the charging cable.

A Power Bank rated 10000mAh will never give the same amount of power when using it to charge a phone,any power bank that can give 70% of stated amount is extremely efficient..
The reason being that the electrical energy stored in the PB are not all released as Electrical energy to the phone,some are converted to heat energy which wastes in the course of the charging and the longer the USB cable the more the energy is wasted..so if you are charging with a PB it's best to use a short cord for energy conservation..