It's not a mismatch when used together.
Kakuzu used Wind style to strengthen the power of his Fire style.
So adding fire to the Rasengan would probably be overkill.
Can't be assed debating this bull anymore...the question is which one would be stronger or win. Answer,same strength roughly.
Rasenshuriken is more cutting and would kill instantly while disabling the enemy. Also it can become projectile..I guess this makes it better.
Rasengan with Enton: Would continue to burn the opponent to death after initial damage is done...but would not be as cutting or initially damaging as Rasenshuriken nor would it be projectile...so in my opinion it would be the worse one of the two....
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About Sharingan...
The Sharingan's third and most well-known ability is that it grants the user the ability to memorise almost any technique that he or she witnesses, apart from other kekkei genkai techniques. The user can memorise ninjutsu, genjutsu, and taijutsu with near perfect accuracy, allowing the user to use the techniques as their own, or even modify them to create their own new techniques, much like Sasuke Uchiha's Lion Combo. In order to reproduce a copied technique, however, one must have the necessary skill or ability to perform them. A prime example is Rock Lee's brand of taijutsu. While Sasuke was able to copy some of Lee's moves, they put a much more significant strain on him since he hasn't trained nearly as much as Lee has. In addition to physical skill and kekkei genkai techniques, the Sharingan cannot reproduce techniques dependent on other factors, such as summons that the user has not signed a contract with.
Blaze Release Rasengan vs Rasenshuriken would be cool. 
