Q: "Invalid" Quicktime Movie Files

Unfortunately you are asking for a solution to a specific problem but not providing enough information to determine what the problem actually is. (I.e., your issue is better approached using a "hands-on" examination strategy by an experienced user.)

Large files that were created in Quicktime and read as "Quicktime Movie" files now read as invalid when I try to open them, yet I haven't changed anything, bar using the current "El Capitan" operating system?

The term "Quicktime Movie" files refer to any MOV file container containing any form of data compatible with the system on which the file was originally created. To be playable on your current system...

1) The file containers and/or compressed data must be uncorrupted,

2) The file containers and/or compressed data must be supported by the embedded structure/player app you are attempting to use, and

3) The player app must be programmed to recognize/handle the combination of file container and compressed data.

Basically, we don't know how your files were originally created, under what operating system they were created, what codecs were used, how the files were copied/stored between the time of creation and current playback attempt, which QT player/embedded structure you are attempting to use for playback on your current system, etc. Most users aren't familiar with, nor are they interested in, such issues. They simply want answers. However, as an "industry professional," I am hoping you might be able to provide enough information to at least determine type of problem you're experiencing here—corruption, codec, security, embedded support structure, player GUI, user account, etc. It would also help to know the specific nature of the "Invalid" modal message. (E.g., an "Invalid Atom" message implies a different set of possible problems than an "Invalid File" modal message.

I've tried using outside software to open them but have failed.

Again, it might help to be more specific here. For instance, different apps rely on different methods of providing system support. E.g., apps like QT 7 and MPEG Streamclip rely on centralized codec configuration support, QT X relies on the more limited but global, pre-programmed playback structure embed while virtually all FFmpeg based apps have codec support programmed within the app itself. Thus, knowing what codecs were used to create a file, knowing how the file was created and knowing which apps will or will not play a file may help to determine if a file has been corrupted or is subject to a security issue stemming from software updates. As a last resort, it might be helpful to simply post a short sample file (if available) for download and analysis by several fellow user's on a number of different systems in order to compare ideas.

Why would a company create software that doesn't recognise files that we created by previous versions of said software. It really doesn't make sense?

Unfortunately, there could be a number of reasons here. The biggest is the fact that QT is in the process of evolving—i.e., being completely rewritten. For instance, the "Classic" version of QT (as represented by pre-QT X apps/structures) is limited to use as a Program Stream (PS) content player. In an attempt to modernize QT X, it was re-written to be a combination PS/TS (Program Stream/Transport Stream) player but, in the process, terminated support for "legacy" codec content. The probably strategy here is to support a limited number of codecs having a wide range of uses rather than a wide range of codecs only having limited, specialized uses. To be sure this represents a trade-off which many long-time QT users do not appreciate. In any event, problems have cropped up under each new QT X "improvement" since its initial release under Snow Leopard and I suspect they will continue to do so.