I know they're far from the same thing as well as anyone, rather what I'm getting at is WoT is an apple and ASoIF is an orange but the question is viewers loved their orange and you could feed them another one but can 'fruit' work on television.
Where they could roughly be considered 'the same' is that in terms of big influential fantasy series in chronological order it goes Lord of the Rings -> Wheel of Time -> A Song of Ice and Fire. Tolkien introduced us to epic fantasy with a hero's journey against a big bad. Jordan took the base template and brought it to a far grander scale with a lot more colour. Martin took the scale and scope but dropped the black & white hero's journey and made everything a more realistic shade of grey with decisions having consequences.
None of these setups are inherently 'better' than the other, the problem is more that when Tolkien black & white hero's journey keeps getting repeated over and over again it gets scale, and Martin's shades of grey is a refreshing change of pace. But if everyone starts copying GRRM then it can just as easily become tiresome grimdark.
Just to ramble on a little more, I like to think if there's a 4th/next big influential series it's Brandon Sanderson's Stormlight Archive. These are my own thoughts, but with what I'm talking about above what I love with Sanderson here is I think he finds a nice middle ground where he drops the black & white and the hero's can go to some dark places, but in the end they don't get their heads chopped off but rather are triumphant, in some inspirational fashion. Or how I like to look at it now, using OT Star Wars if Martin is Dark Vader chopping freezing Han in carbonite and chopping off Luke's hand, then Sanderson is Anakin Skywalkers redemption, that solemn gaze as Palpatine is killing his son and then stepping forth to save him.
I'd also argue that Stormlight Archive has more in common with the other two series than it does with Game of Thrones, but the characters tend to be more accessible and likeable than LoTR and WoT whereby their thoughts and speech mannerisms tend to be more informal and more consistent with the present day.
I've read pretty much all of Sanderson's work, and while Stormlight Archive is likely his magnum opus, and is an exhibition in world building and magic system crafting, it's still consistent with his other works including the Mistborn books that are relatively easy reads. As far as a challenge level, obviously they are large books but I think they could be easily read by young adults. I'm not trying to be critical, it's just more emblematic of his style and a big reason why he is popular IMO: his stories are "fun". He's sort of like the Joss Whedon of fantasy (before all the controversies).
I'm very impressed with the fact that he did manage to conclude Jordan's series in a manner that was really consistent with Robert's style, rather than his own, which takes a lot of discipline and respect for the original material IMO. It's like the opposite of what happened with Benioff and Weiss.
Meanwhile, Game of Thrones deliberately under-emphasized the fantastical elements, focusing more on a gritty, medieval drama with female characters largely constrained by historical limitations, no outright wizards, few references to other humanoid races of any kind, and with the White Walkers, dragons and some of the religious elements largely occupying that niche alone. Characters are rarely flippant (aside from Tyrion) and their interactions have that formal edge to them in keeping with their station.
Speaking for Mrs_NyQuil, who is not a reader of fantasy, she enjoyed GoT precisely because of the intrigue, backstabbing and family drama, and was less inspired by the fantastical elements which ramp up as the seasons go on. I think a big reason behind its universal success is that while it is inherently a fantasy work, those traditional elements take a backseat for the most part to a soap opera on a grand scale, which appeals to a wider audience.
Personally I think the biggest supporters of Wheel of Time will end up being Robert Jordan readers who enjoy seeing the visuals of what they may have imagined all along and can fill in the gaps in the storytelling with their own knowledge of the book series.
Whereas, with GoT, there may well be more fans of the HBO show out there than of the books themselves, which is quite the accomplishment for any converted fantasy series.