On the original topic, are we debating something that cannot be measured?
I confess that I am not enough of a fantasy fan to judge.
The Wizard of Earthsea might be more like LOTR than Conan simply because there is not lots of sword swinging but is that enough to say it is influenced significantly by Tolkien? I would not describe the two fantasy stories I have read by Bujold as similar to either.
There's a bit on Le Guin's wikipedia page which states the Lord of the Rings had an enormous influence on her simply by showing her what was possible in the fantasy genre.
And I think that encapsulates the biggest influence Tolkien had on the genre. The scale on which most fantasy authors build comes from Tolkien. It's not that Tolkien invented long lengthy books and series in which large parties of characters adventure across most of the hugely detailed world, but he made it hugely popular. We may reject his themes of good vs evil, his non-human races, his innocent heroes and quests and on and on, but most of the big names in fantasy are building on Tolkien's scale.
If I had to pick one more concrete trope that I think Tolkien is largely responsible for and that is still hugely popular in the genre, it is the concept of wizards being protagonists/mentors to protagonists, particularly in the mysterious benevolent Odinic mould that Gandalf is from. A lot of the early significant fantasy writers have wizards as sinister enemies or distant patrons.
Any hoo, it's tricky working out what the correct measuring scales are (and trickier to go measure them), but yes I think this is measurable. Look at the various "Top X" books and ask yourself which feels more like which, look at book sales, look at movie profits, look at which author is mentioned more on book covers (if you're really sad), or google references to each author on major fantasy sites/national newspapers (if you're even sadder) and I think you'll start to get a good if rough idea of who's more influential.
Not that I can be bothered to do that as everything I've heard and seen says this is like asking if you want to have a fist fight with a special forces soldier or the unholy splicing of Bruce Lee, Mike Tyson and a Silverback Gorilla.