I don't have onew but was considering getting one some time ago and was researching...
I have 2 other Brymens for few years and they seem to be good quality so far.
Simplest way to explain the difference is that BM887 is feature complete meter with Hi pot tester, and that BM878 is more HI pot tester, Earth current tester with slightly limited multimeter functions.
BM887 :
20Khz AC BW
current ranges from 600µA to 10A
BM878
Earth continuity
Hi pot resistance
Hi pot resistance GO/No GO (compare mode)
Hi pot PI / DAR (Polarization index & Dielectric Absorption ratio measurement)
current ranges only 60/600mA
BM878 is more complete Hi pot tester and also Earth cont. tester. If you need Hi Pot tester primarily, that that is the one to have.
BM887 is full multimeter with 1000V resistance mode. I guess that is for people who need a full meter and they occasionally want to cursory check if some device's insulation still holds hi pot....
Those were my conclusions...
In meantime I got a very good price on other HiPot meter and never have bought the BM878.
Best,