ICE40LP384-SG32 is supported by IceCube2. The IceCube2 is rather a pretty basic tool, it works with 384 fine (tested). The integrated Synplify Pro (quite hidden, needs to be started via Tool->Tool options..) allows RTL and Technology views.
The iCE40UP3k/5k are supported by IceCube2 and Radiant. Radiant includes the same as the IceCube2 one, plus Reveal Analyzer (something like X's ChipScope), built-in Diamond programmer, an useful editor, Netlist analyzer with graphics view, etc..
The IceCube2 generates smaller and faster design (most visible with larger designs) than the IceStorm does, it can infer ie. multipliers with built-in DSP modules (UP5k) etc. The IceStorm is less effective, and infers ie. multipliers in fabric (you have to instantiate the modules/primitives manually).
Generally you need 2-3x more LUTs with iCE40 compared to the X's Spartan6, I would guess. Also iCE40 is low power and therefore slower than the Spartan6.