Both Goldberry and Ioreth are more “main characters” than, say, Arwen - more lines & more plot pertinence.
This Mohs scale is awesome; I hadn’t seen it before, and it leads me to my comment.
Both Tolkien and ST (Roddenberry, Berman, Sternbach, Okuda) in their own ways, worked hard to create an internally consistent, immersive universe in which what you watched unfold in the story was driven in ways large and small by what came before.
I can clearly recall an episode at approximately the age of 12 when a hand (my mother’s) waving in front of my face snapped me back to reality from reading LOTR. She was trying to get me to go wash my hands for dinner. I realized, in a dim way, that I wasn’t reading the story, I was in the scene.
I can’t recall any other experience in my life where a fictional world drew me in at that level.
I was 7 when Star Trek debuted, and all my friends and I watched it faithfully. Went to my first Star Trek convention in '74. Made many friends, and first connected with my wife, thanks to Star Trek fandom.
I had one friend in high school who was a big Tolkien fan, and he and I used to debate the merits of *LOTR *vs. the *Dune *trilogy. I didn’t get around to reading the trilogy myself until my mid-thirties, and I honestly don’t remember a whole lot of it. Fell asleep during the first movie, and watched the second on DVD.
So, from a purely selfish perspective, losing Tolkien would have almost no noticeable effect on my life, but losing Roddenberry would have deprived me of a lot of pleasure.
Now, if the choice had been between Jerry Siegel and Charles Schulz… *that *would be a tough call.
LotR is literature, star trek is entertainment. Tolkien spent his entire life coming up with the backstory and what ultimately became LotR. Roddenberry kicked out a pilot in what, 2-3 years?
Tolkien looks at questions of man’s humanity, the nature of good and evil, the difference between the eternal and the profane.
Star trek has humans constantly ignoring their own prime directive and is a speciesist space opera.
The world would be a better place without star trek.
According to the OP, both works were around in the past, and had their influence, and all the works they influenced are still around, but the influence has been taken out somehow - I interpret this the meaning anyway.
It is indeed hard to tell whether overwhelmingly influenced works (such as Shannara, or fanfics) would still exist, and if so in what form. I’d tend to speculate that the fictional-works-removal-ray would substitute the nearest equivalent. Maybe Shannara would be greatly influenced by Eddison or Lewis instead. Fanfics of Trek would turn into fanfics of some other TV show: Buck Rogers, Dragnet, Battlestar Galactica, whatever had characters close enough to fit.
Possibly the influence when less direct would remain, and we just wouldn’t recognize it because we didn’t remember the source anymore. Maybe Shannara wouldn’t change at all, but just seem much more original 
Only the things backed up on Europa would be removed entirely from memory, is what seems like the intent was.
Given that intent, I say take em both. I’d like to see what James Blish wrote instead of the Star Trek novelizations - which were what got me to like Star Trek as a kid… I didn’t enjoy it on TV, but Blish’s version was amazing…
If the results don’t turn out as desired, put them back and take something else 
Considering how much inspiration Lester del Rey noticed went into the first draft, probably not. (Apologies if it’s hard to read; it’s a photo.)
As for the issue at hand… I think it may depend on the role Star Trek actually played in race relations in the U.S. at the time it first aired. LOTR is great literature and all, but did it help end lynching?
How about we just get rid of Skald?
Actually, Star Trek is very moralistic and uses each of the main characters as a sort of archetype of different elements of humanity. Spock is all logic, McCoy is sort of the opposite of that, Kirk is all instinct, etc. Individually, none of the characters ever carries the day–they all need one another and none are really expendable. The individual stories, too, dissect various social issues as well and at least pretend to validate controversial positions. It’s actually pretty deep for what and when it was. But still I’d cut it to save LOTR.
Ahem:
Ooh! Ooh! Get rid of Tolkien! Yes!
Seriously, I would be happy for LOTR not to exist.
Not that I’m really terribly committed to saving either.
That is just Tolkien’s opinion, and we all know he had a tendency to make things up when it suited him.
Although I enjoy, personally, Star Trek way more than I’ll ever enjoy Tolkein, I can easily admit that Middle Earth is the greater contribution to fiction. He popularized and started so much of everything that is that genre that without it, we’d have so little mythology. Sci-fi however would easily live on without Trek, and Trek isn’t even the best that sci-fi has to offer, (whereas Tolkein is easily the best that fantasy has to offer).
Set phasers to kill, I say. Bye bye, Star Trek.
Dear Skald –
If we get rid of Trek, we’re stuck with Star Wars and all it derivatives!
But if we get rid of Tolkein, we’re stuck with Thomas Covenant and Sword of Shanana and THEIR derivatives!
Please have mercy! Would it slake your evil thirst if we (gladly) gave you Game of Thrones? Most of them end up dead anyway.
Beam
Torches lit!
Asimov??? Easily dispensed with. Arthur C. Clarke had better science, and Heinlein had far better characters and story lines. Asimov was interesting, and I loved Foundation until he had to infect it with his da^^ed robots. But his writing technique was to type a story from start to finish at 110 wpm, type a second draft to correct spelling errors, and send it off. It showed.
Beam
I have made a note of your insolence and have dispatched a quartet of throttle-bots to discuss the matter with you.
In my time there was far too much overlap among LOTR and ST fandom for such a distinction to be possible.
Is this a real poll? And who are these people who would rather have Star Trek than Middle Earth? Seriously?!
Next we’ll have to choose between the Sistine Chapel and some kid’s stick-figure drawing of his dog.
Lose Star Trek. And you can take Dr. Who as well.
I think men are more broadminded when it comes to works of the imagination: there are many — not me since I get bored quickly — who can become enormously enthralled watching or reading plots set in institutions, schools, jails, private islands etc., where men are non-existent.