Drawbacks of changing a standard voltage-current converter to amplify the signal?
They both have similar compliance (very slightly more for #2)- they'll saturate at around 37mA. 

The gain is a bit different between the two circuits. 

Circuit #1 has a voltage gain of 3 and a sense resistor of 100 ohms so 1V in gives you 30mA current (minus a fraction of 1% for the transistor gain). 

Circuit #2 will sink 31mA for 1V in (minus a fraction of 1% for the transistor gain). That's because the divider network loads the sense resistor, reducing the effective value to ~96.77 ohms.

Circuit #2 divides down the feedback signal so it may be noisier, all other things being equal (though the noise from the first op-amp may compensate if you don't filter it).  



As an alternative, consider reducing the sense resistor to 33.3 ohms and scrapping the divider network. Then 1V in gives you 30mA. If the saturation at 37mA is desirable, add a suitable resistor to the collector side. 

Normally the variable resistance load would be in the collector side (the 220 ohm resistor).