What is the most optimal way to concat XML files as one large string/text file?
functions
Your script does a few things

iterate over the files
recursively iterate over the subdirectories
parse the files
concatenate the results

Better would be to separate those in different functions.
The extra advantages is that you can test these functions separately, you can document them with a docstring, and add typing information
comments
You comment what the code does. Python is luckily so expressive that almost anyone can understand what a particular line does. what is more difficult is the why you do certain steps, and why you do them in a certain order. This is what should be commented
global variables
Your big_file method changes the global state of the program. That makes it more difficult to reason about, and also makes it difficult if you want to use this methon on 2 separate directories. Here you append to big_text. If you want to keep it like this, I would pass it on as a function parameter, instead of a global variable
def big_file(path, big_text = None):
    if big_text is None:
        big_text = []
    
    ...
            big_file(path + '/' + i, big_text=big_text) 

pathlib.Path
Most file operations are simpler when using the pathlib  module. It will be a lot more robust than manually concatenating paths like in path + '/' + i
error handling
You have a try-except block with a bare except. Better here would be to catch the errors you expect specifically and handle those, and let other, unexpected error bubble up. Fail hard, fail fast, instead of covering up bugs can help you write more stable and correct software
logging
Instead of using print, you can use the logging module. That way you can make a distinction between different levels of importance, and filter some out if needed
generators
To prevent a MemoryError you can use generators. these are special functions that do their work piece by piece, and can work without keeping the whole structure in memory
You can have 1 generator generate the files
def iterate_files(path: Path) -&gt; typing.Iterator[Path]:
    &quot;&quot;&quot;Recursively iterates over `path`, yielding all the correct files&quot;&quot;&quot;
    for file in path.glob(&quot;*&quot;):
        if file.is_dir():
            yield from iterate_files(file)
        else:
            # or a check that the file has a certain suffix
            yield file

Then you feed this iterator to the parser generator
def parse_files(files: typing.Iterator[Path]) -&gt; typing.Iterator[str]:
    &quot;&quot;&quot;Parse the xml files.&quot;&quot;&quot;
    for file in files:
        try:
            xml = ET.parse(path + '/' + i).getroot()
            yield ET.tostring(xml, encoding='unicode')
        except &lt;stricter exception&gt;:
            logging.warn(f&quot;error in {file}&quot;)
            raise

In the last except, you can have different except blocks with different result
You can then feed this to another generator which writes it to a file:
def write_to_file(
    text_iterator: Typing.Iterable[str], output_filehandle: typing.TextIO
) -&gt; Typing.Iterable[str]:
    for chunk in text_iterator:
        output_filehandle.write(chunk)
        yield chunk

putting it together
if __name__ == &quot;__main__&quot;:
    path = Path(&quot;PLC 2360&quot;)
    files = iterate_files(path)
    parsed_filed = parse_files(files)
    
    with Path(&lt;output_path&gt;).open(&quot;w&quot;) as output_filehandle:
        parsed_filed_after_writing = write_to_file(
            text_iterator=parse_files, output_filehandle=output_filehandle
        )
    ...

In that last part, I've opened the file in the main part of the script, taking into account the principles of clean architecture