Current source schematics. What's the difference?
This is really far from being a practical circuit- too sensitive to resistor ratios, it's also not quite constant as it neglects the loading effect of the resistors on the "output". Very slight offset voltages on the op-amp will swamp your feedback. 

But your proximate problem with almost ideal parts, as the comment from @Marko indicates, is the gain of the LTspice op-amp, which is default at 100,000 so with the left circuit it takes 100uV error to drive the output from 0V to 10V, which is basically your entire feedback signal with that 0.1 ohm sense resistor. 

The other circuit has an extra gain of 100, so that source of error is reduced.