Hey there! Creator of Inazuma here!
I've had many people ask me this question before via DMs or on Discord so I figured that I'd make some sort of official post regarding the answer to this.
Lets get one thing out of the way: Game SMS easily beats Game Inazuma. SMS was designed to be gamebusting overpowered with a million moves and ways to destroy levels while Inazuma was meticulously and specifically designed to engage with SRB2's leveldesign proper.
Now for the tricky one... LORE SMS vs LORE Inazuma:
Lore SMS vs Lore Base Inazuma would actually be a very interesting fight since lorewise, Inazuma is meant to be near the level of Super Sonic in terms of feats and abilities. Based on what GoldenShine has said in the past, Super Mystic Sonic lorewise is specifically not as strong as Super Sonic.
Because of this... Ultimate Inazuma would easily beat Super Mystic Sonic in a battle with extremely low difficulty. Ultimate Inazuma is always meant to be a character that far and beyond surpasses the likes of even Hyper Sonic and since SMS is weaker than Super Sonic... well, you know.
A much more interesting battle I think would be Hyper Mystic Sonic VS Ultimate Inazuma:
Ultimate Inazuma has incredible dimension ripping powers and has the ability to speed blitz opponents with time stopping abilities. He is also incredibly resilient able to take on attacks comparable to multiple supernovas. Not only that, there is no time limit to Ultimate Inazuma's form. He can maintain the form indefinitely without any loss in stamina (SRB2 Ult Ina has reduced ring drain for the sake of balance but also as a nod to his lore). However...
I recall GoldenShine saying that Hyper Mystic Sonic has infinite speed and energy with Sonic's limit in that form really just being his imagination as well as the time limit that the form has.
Hyper Mystic Sonic no matter how you slice it will always speed blitz Ultimate Inazuma and depending on HMS' output, Ult Ina might not be able to take on all of Hyper Mystic Sonic's attacks...
BUT! There is a critical difference between the two; Ultimate Inazuma does not have a time limit while Hyper Mystic Sonic does... and its very short. From what I recall GoldenShine stating, Hyper Mystic Sonic has immense energy drain meant to reference the likes of SSJ3 Goku and can potentially implode due to how much energy his body is amassing. The form is very dangerous and has severe consequences if Sonic doesn't use it properly.
So in this sort of situation it really goes down to "Can Ultimate Inazuma last long enough before HMS selfdestructs?"
To that question.. I think we should look at the personalities of Inazuma and Sonic. Sonic is a trickster, yes, but he plays fair and is very honorable. He's the 'Knight of the Wind' afterall. While Sonic can fight, fighting is more of a secondary thing for him. He's not actively trying to fight people he moreso treats it as a sport and uses violence only when necessary. Inazuma, on the other hand, is a martial arts master way more skilled than Sonic who has barely received any training. Inazuma has a very keen battle sense and has incredible adaptability which is how he's able to fend off against monsterous foes back when he was crippled. Inazuma is also very much NOT honorable and will more often than not resort into using cheap tricks and tactics to win fights. Because of this, I can see Ultimate Inazuma using his enhanced speed and durability to disengage and outlast HMS up until the point HMS self destructs from the sheer amount of power he amassed. Of course, HMS can also speed blitz and try to end the fight by ramping up enough power to take Ultimate Inazuma out. However, like I said before, Inazuma's battle sense and adaptability will most likely kick in and make him react accordingly into not letting Sonic power up enough to take him out. And as we already know, Sonic is very reckless and does actions first and thinking later. I don't think Sonic, especially in his stressful powered up state, would be in a stable enough state to properly outplay Inazuma's cold meticulous calculative actions. Because of this, I think Ultimate Inazuma vs Hyper Mystic Sonic is an incredibly close match with the winner really being whoever the author wants to win but with a slight edge towards Ultimate Inazuma. However in terms of pure power, Hyper Mystic Sonic is definitely way way stronger than Ultimate Inazuma.
Hope this answers your question! I do not own Super Mystic Sonic so things that I said may be off. Feel free to correct me if need be!