For the smaller trial, you would need to worry about imbalances. But that is why it is important to do a variety of sensitivity analysis as the FDA statisticians always do. But remember that this is clinical data and often there are also other sources of data outside of the immediate trial that can provide corroborative evidence.
????? p-value is a measure of the amount of imbalance possible in random draws. Same p value for different size trials means same chance of imbalance.
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