The 87 III does have some features that the 87 V is missing. The autoranging is much faster. But the main thing is, the 87 III's bar graph (actually an analog pointer) has 6 times the resolution of the 87 V's bar graph (1000 counts full scale vs. 6000 counts full scale). I'll keep mine for that reason alone.
In the original 80 series, the 83, 87 and 88 all had different LCDs. The 83 had a regular bar graph that is just a full scale reading of the current range. The 87 had the high resolution analog pointer (4000 counts, wrapping four times for each range). The 88 had yet another type, a 2000 count analog pointer, wrapping twice per range. So the high res pointer was actually a big feature that distinguished the 87 from the cheaper 83.
Probably to save money in production, on the 80 V series, the 83 V, the 87 V and the 88 V all use the same LCD. So you only get the regular 6000 count bar graph.