My take...staying entirely within the Land of RAW:
1 - "Simulacrum creates an illusory duplicate of any creature." - so there is nothing to prevent duplicating a Solar (though the Solar migh get pretty irked)
2 - "Effect one duplicate creature" - So it can be affected by Magic Jar..I see nothing in Magic Jar that discusses type.
The creature will have "half of the real creature’s levels or HD and the appropriate hit points, feats, skill ranks, and special abilities for a creature of that level or HD)."...a lot of fudge factor here, as there is no discussion of Stats. Personally, I'd say Stats are the same, but the GM would be entirely within RAW to reduce stats by 1/4 HD lost...still, probably pretty good.
But there is where it gets significantly less cool. From Magic Jar:
"You can’t choose to activate the body’s extraordinary or supernatural abilities. The creature’s spells and spell-like abilities do not stay with the body."
So you'd get the STR/DEX/CON/Hit Points (modified by the level loss, possibly) but not much else, really.