The darker more complicated parts of Trigger's story were concentrated in the 12,000 BC time period, which, not coincidentally, was the part of the game that was designed by the guy who was later in charge of Chrono Cross.
I hated the alternate dimension thing (with only two dimensions and them being almost exactly alike)
I actually really liked this aspect of the game, a lot of the differences were subtle and clever. Like how at the beginning when you're lizard hunting in the Home dimension, you ambush a lizard from a ledge, then when you go through the same area in the Another dimension a.k.a. Soviet Russia, the lizard ambushes you.

Loved the alternate versions of each town's music too.