is it bad to have many different measurements for the same target variable?
Note that you are solving two different problems here. 

In the first problem, you want to predict the target variable given one noisy measurement. 

In the second problem, you want to predict the target variable given some statistics from a group of noisy measurements. 

Your results show that the second problem is easier to solve which is intuitive, since the amount of noise (variance) for average of multiple measurements is less than only one measurement (closely related to Law of Large Numbers), thus the relation in the second problem is easier to find by the model. 

Therefore, if both problems are equivalent to you, go with the second problem which is easier to solve.