Two FizzBuzz solutions
As has already been pointed out, creating a list is preferable as it avoids the concatenation of large strings. However neither of your solutions is the most pythonic solution possible:

Whenever you find yourself appending to a list inside a for-loop, it's a good idea to consider whether you could use a list comprehension instead. List comprehensions aren't only more pythonic, they're also usually faster.

In this case the body of the loop is a bit big to fit into a list comprehension, but that's easily fixed by refactoring it into its own function, which is almost always a good idea software design-wise. So your code becomes:

def int_to_fizzbuzz(i):
    entry = ''
    if i%3 == 0:
        entry += "fizz"
    if i%5 == 0:
        entry += "buzz"
    if i%3 != 0 and i%5 != 0:
        entry = i
    return entry

fizzbuzz = [int_to_fizzbuzz(i) for i in range(start, end+1)]


However, while we're at it we could just put the whole fizzbuzz logic into a function as well. The function can take start and end as its argument and return the list. This way the IO-logic, living outside the function, is completely separated from the fizzbuzz logic - also almost always a good idea design-wise.

And once we did that, we can put the IO code into a if __name__ == "__main__": block. This way your code can be run either as a script on the command line, which will execute the IO code, or loaded as a library from another python file without executing the IO code. So if you should ever feel the need to write a GUI or web interface for fizzbuzz, you can just load your fizzbuzz function from the file without changing a thing. Reusability for the win!

def fizzbuzz(start, end):
    def int_to_fizzbuzz(i):
        entry = ''
        if i%3 == 0:
            entry += "fizz"
        if i%5 == 0:
            entry += "buzz"
        if i%3 != 0 and i%5 != 0:
            entry = i
        return entry

    return [int_to_fizzbuzz(i) for i in range(start, end+1)]

if __name__ == "__main__":
    start = int(input("Start Value:"))
    end = int(input("End Value:"))
    for i in fizzbuzz(start, end):
        print(i)


(Note that I've made int_to_fizzbuzz an inner function here, as there's no reason you'd want to call it outside of the fizzbuzz function.)