With high electric vehicle (EV) adoption, optimization of the charging process of EVs is becoming increasingly important. Although the CO2 emission impact of EVs is heavily dependent on the generation mix at the moment of charging, emission minimization of EV charging receives limited attention. Generally, studies neglect the fact that cost and emission savings potential for EV charging can be constrained by the capacity limits of the low-voltage (LV) grid. Grid reinforcements provide EVs more freedom in minimizing charging costs and/or emissions, but also result in additional costs and emissions due to reinforcement of the grid. The first aim of this study is to present the trade-off between cost and emission minimization of EV charging. Second, to compare the costs and emissions of grid reinforcements with the potential cost and emission benefits of EV charging with grid reinforcements. This study proposes a method for multi-objective optimization of EV charging costs and/or emissions at low computational costs by aggregating individual EV batteries characteristics in a single EV charging model, considering vehicle-to-grid (V2G), EV battery degradation and the transformer capacity. The proposed method is applied to a case study grid in Utrecht, the Netherlands, using highly-detailed EV charging transaction data as input. The results of the analysis indicate that even when considering the current transformer capacity, cost savings up to 32.4% compared to uncontrolled EV charging are possible when using V2G. Emission minimization can reduce emissions by 23.6% while simultaneously reducing EV charging costs by 13.2%. This study also shows that in most cases, the extra cost or emission benefits of EV charging under a higher transformer capacity limit do not outweigh the cost and emissions for upgrading that transformer.