Find the Maximum Sum of a Contiguous Subsequence in a List
The first solution is quite fine, with minor issues:


It doesn't support empty list
Instead of for i in range(1,len(arr)):, it would be simpler to for value in arr[1:]:
Formatting and function naming doesn't follow PEP8


Given that the first solution is simple and efficient,
I don't see much point in a second solution that uses \$O(n)\$ extra storage.
Other minor issues with it:


It's strongly recommended to use consistent indent width (preferably 4 spaces)
It's recommended to use a line break after the : in a if cond: statement
If you are using Python 3, then use range instead of xrange
Some comments above for the first solution apply here too


Finally, the testing code is overcomplicated, when much simpler alternatives are supported out of the box, for example doctests:

def maxSubArraySum(arr):
    """
    &gt;&gt;&gt; maxSubArraySum([6, -1, 3, 5, -10])
    13
    &gt;&gt;&gt; maxSubArraySum([5])
    5
    &gt;&gt;&gt; maxSubArraySum([])
    0
    &gt;&gt;&gt; maxSubArraySum([-1, 1, -3, 4, -1, 2, 1, -5, 4])
    6
    """
    ...