Old quickSort vs new one

def quickSort(listToSort):
    """Sorts listToSort using the QuickSort algorithm - technically broken"""
    pivot = listToSort[len(listToSort)//2]
    lowerList = []
    higherList = []

    for i in range(len(listToSort[1:])):
        if listToSort[i] <= pivot:
            lowerList.append(listToSort[i])
        elif listToSort[i] > pivot:
            higherList.append(listToSort[i])

    #if all values equal each other, make checkValues false
    checkValuesLower = not all(x == lowerList[0] for x in lowerList)
    checkValuesHigher = not all(x == higherList[0] for x in higherList)

    if len(lowerList) > 1 and checkValuesLower:
        sortedLowerList = quickSort(lowerList)
    else:
        sortedLowerList = lowerList

    if len(higherList) > 1 and checkValuesHigher:
        sortedHigherList = quickSort(higherList)
    else:
        sortedHigherList = higherList

    return(sortedLowerList+[pivot]+sortedHigherList)

def quickSort2(listToSort):
    pivot = listToSort[0]
    lowerList = []
    higherList = []

    for i in listToSort[1:]:
        if i > pivot:
            higherList.append(i)
        elif i <= pivot:
            lowerList.append(i)

    checkValuesLower = not all(x == lowerList[0] for x in lowerList)
    checkValuesHigher = not all(x == higherList[0] for x in higherList)

    if len(lowerList) > 1 and checkValuesLower:
        lowerList = quickSort2(lowerList)
    if len(higherList) > 1 and checkValuesHigher:
        higherList = quickSort2(higherList)

    return(lowerList+[pivot]+higherList)