I think, for the two guitars compared here, the Jackson SL1 would be your best (read most sensible) bet. The JS1000, despite having the trem of champions, doesn't really match your criteria.
However, for the sake of argument, I think you have compared two guitars intended for completely different purposes. Jackson SL1 - 80s metal. JS1000 - Joe Satriani. The JS1000 is not really meant to play heavy metal. Sure, neither was a Les Paul and I'm sure you could, but a more accurate comparison would be between the Jackson SL1 and the Ibanez RGT3120, a guitar that (spec-wise) seems to have been deliberately designed to match the Jackson Soloist. Both sport fast thru-necks and good trems. Beyond that, it's ice cream (appearance, trem type, body wood and sound).
Between the Ibanez RGT3120 and the Soloist, I'd take the RGT; if only because I don't like the Jackson's headstock, body shape, trem, pickups and the colour (all subjective, mind). Not because I'm a die-hard Ibanez fan.
The solution? Play them both and see one which you like most. Either way, you'll have fun deciding.