I seem to have this compulsion to buy Doom over and over again. I own it on disc, I own it on steam, I own it on Xbox original, 360, and 360 arcade. Despite the multiple purchases, I generally only play it using the ZDoom or GZDoom source port. Now that GOG has Doom (again?), is there any real reason I should re-purchase it?

In a nutshell: Are there any differences between this version of Doom and the Steam version of Doom that would warrant a re-purchase?

If you use a sourceport you only need the WADs, which should be the same wherever you bought them from.
I highly doubt the WADs differ bewteen Steam and GOG versions.

Like you, I own several physical copies of the game, and this is my third digital purchase of it. (I bought it direct from id's site, back when they had their own download store, later on Steam and now here.) It is the only game that remains permanently installed on every machine I own. It's my "desert island" game, pretty much, and I have spent more time and money on it than what you could call reasonable by any stretch.

The versions sold here are packaged with DOSBox, like on Steam, the only difference being the aforementioned rare patched version of Final Doom, which was previously, if I'm not mistaken, only available as part of the id Anthology collector's set. There are fan patches to update your Steam version. The main reason to get these games here, is for convenience. And of course, to show Bethesda that drm-free is life, drm-free is love. :-)

It seems to run better. I think GOG are better with Dosbox then Steam.

There's a good chance this is true. GOG uses a much newer version of DOSBox than Steam distributes.

For what it's worth, though, you might try Chocolate Doom for a vanilla experience without the disadvantage of an emulation environment that DOSBox is. Instructions for running it are here: http://doomwiki.org/wiki/How_to_download_and_run_Doom#Ultimate_Doom.2C_Doom_II.2C_and_Final_Doom
(on Windows, this is super-easy since it automatically detects the GOG version and uses it)

Wow awesome, 5k support! thanks for showing that to me. maybe this should be part of the default package. It does a better job then dosbox.

For the most part I use Zdoom, but when I'm feeling retro, Chocolate Doom is my go-to.

Not really.

There is one interesting difference, though: the GOG version of Final Doom is the bugfixed one (forgotten multiplayer starts have been added, the famous yellow key from TNT MAP31 is not missing in single player mode, etc.) while the Steam version of Final Doom is the old with all these bugs. Of course the community has long had patches allowing to update the bugged version to the fixed version, so you don't need to pay to get this.

Also the GOG Dooms have PDF scans of their manuals along the goodies. There's also a PDF copy of the Doom Bible among the Ultimate Doom goodies, but you can also get that from Doomworld for free.