Both the F-104G and Mirage IIIE are quoted on wikipedia (yeah, yeah, I know...) as having a maximum bomb load of around 1800 kg, though stats for the later F-104S suggest the type was able to lug an additional 1000 kg to a useful range (though, in practice this extra warload saw little use).In the non nuclear role the f104 might be too limited. IIUC in Vietnam USAF F104 carried a pair of 750lb bombs and I think the Mirage carried significantly more than that.
Combat radii are about the same, given the lack of clarity about mission profile and load
Mirage III claims a longer ferry range by about 400 km. Again, the actual load-out is unclear... we may be comparing one clean vs the other with tanks.
Superficially, the F-104, particularly if you can pick up the '-104S looks much better.
The F-104G has no BVR capability and could lug four IR guided WVR missiles, while the Mirage III nominally has BVR capability but in practice the R.530 proved a total mess, and it's also limited to two WVR missiles. The F-104S, in service from '69 but with a prototype flying in '66 and earlier design studies... well two Sparrows and up to six Sidewinders make it pretty clearly better in the air to air role.