i have the same problem, after some test, i think my battery is fine, it cause by OS or charge software.
updated from 8.1 to wp 10 few weeks ago, then i faced this problem, it was not seen by wp 8.1.
this week i use aida64 to watch the process of charge, according the basic knowledge of li-on battery, if charging Amps lower than 100ma, the charge-chip will shut the charge process off, and think the battery is now fully charged.
aida64 can show charge rate of battery, shows it as mw, mw=ma*v, fully charged li-on battery has voltage of 3.8v, it means when charge rate lower than 400mw lumia 1520 will shut the charge off, and shows 100% fully charge of battery.
but during the observation i found, in wp 10, it the charge rate can be lower than 400 mw by 80% charge, and than suddenly shows 100% fully charged.
that cause the problem, actually it is only 80% charged, but shows 100%.
if the battery is defect, we will see the same problem, but i test it another way:
when charge rate is below 1000mw, i stop charge, and use phone for 5 to 10 minutes to waste 2% battery, then charge it again, it will start from 3500mw charge and slowly down to 1000mw, Continued for half hour, in this half hour it will charged from 78% to 85%, i repeat this method, finally get my 1520 really fully charged.
before i get 100% to 80% for about 10 minutes using, because it is not really 100% charged, only the charge Amps lower than 100ma,and just 80% been charged.
after this method, i get very normal Experience just like by wp8.1, no more suddenly turned off by 20%, or very quickly from 100% down to 80%.
but it will not fix the problem, i must use this method by every charge, otherwise, using normal charge, it will just be charged for 80% or 70%, and shows 100%.
the perfect charge process for li-on battery is: first high Amps about 1.5a or 2a for a little while, then lower about 1a for a long time untill it be charged for 85%, in the end from 85% to 100% using very small Amps under 500ma to protect battery, when it is lower than 100ma, the chip will shut off charge.
the problem by wp10, it reachs 100ma too soon, but it is not really fully charged, when you use your phone for minutes, and charge it again, it will be charged again from 1a down to 100ma for a while