Both of them took responsibility for others. Toomes was committing crime in order to improve his families life, as well as his own. Peter was saving people and being a hero, which was coming at the expense of his own life, as he was leaving parties early, ignoring calls from his aunt, getting in trouble at school and leaving the girl he liked in order to stop crime.
Both were being denied what they wanted by the elite (i.e. Tony Stark). Toomes felt the system was against him and that he was being denied opportunities due to the likes of Stark, hated him, and felt he had to do desperate things to be able to provide for his loved ones. Peter on the other hand, thought very highly of Stark, wanted to be like him and was desperate to join him in the Avengers.
In a way, Toomes is like a dark version of what Peter was in Civil War when his main goal was to look out for the "little guy". Toomes was also doing what he was doing to provide for the "little guy" (i.e. his family and himself, and while he didn't mention them as his main motivation, he was also providing for the people working with him). Toomes even admired Peter and saw a bit of himself in him too, as he felt Peter understood what he meant when he spoke about doing anything for his family and having to pick up after and do the dirty work for the likes of Stark.
Toomes was willing to do whatever it took to achieve his goal, including killing people if necessary. Peter desperately wanted to avoid killing, and kept refusing to use his suits instant-kill mode. It should be noted that Adrian did spare Peter for saving his daughter, and he may have kept his identity secret at the end of the movie because Peter saved his life too, so he did have some honour.
It was fitting that part of the final fight between the two took place in the sky, as for most of the movie, Peter was aiming very high, wanting to join the Avengers. IMO, it was even more fitting that the fight finished on the ground, as that is ultimately where Spider-Man belongs and is needed now. He is needed to protect the "little guy" from the likes of Toomes, and maybe even help and prevent other people from becoming desperate like Toomes, feeling the only way they can provide for loved ones is crime.