Without spiling the future plot too much, what influences and traits will Shouto end up adopting from Tsuna?
Tsuna would definitely help little Shoto hate himself a lot less and open to asking for help from others. At this point, Shoto dislikes Enji but for more "slow burn"(?) reasons: Endeavor is a shit mentor, Shoto can tell Endeavor is the root of most of the family's conflict and disunity even if he was never told explicitly what happened, and he's aware that something is wrong with their family dynamics even if doesn't know exactly what. Stemming from this, Shoto has a sense of responsibility and desire to be loved as implied when he blames himself for his burn in canon. By having someone who will listen without judgement, Shoto will have a much healthier outlook on himself and others.
Combat-wise, Shoto will have much more balance between his Quirks. Obviously he'll be able to use them both but in canon, Shoto brute-forces his Quirks cause honestly? It works in most situations. Within UBS however he'll have dexterity and greater control -- able to manipulate both the temperature and shape of his Quirks.
On a little more light-hearted note, Shoto may pick up linguistic habits and mannerisms from Tsuna. He's a perceptive child and Tsuna's mafia tendencies can't be hidden completely. And he'll definitely have more respect for underground heroes!