One major difference is that Demetrius is portrayed as a bully and physically aggressive, while Lysander is characterized as being sensitive and respectful.
We see Demetrius being portrayed as physically aggressive when we see him charge into the woods with the intention of finding Lysander and slaying him. We see Demetrius's intentions to kill Lysander in his lines, "Where is Lysander and fair Hermia? / The one I'll slay, the other slayeth me" (II.i.192-193). While Lysander could just as easily kill Demetrius as well, Lysander is choosing to be passive and running from Athens with his loved one instead. We also see Demetrius act as a bully in his treatment of Helena. In fact, Demetrius is absolutely abusive towards her. He threatens her with violence as we see in his lines, "Tempt not too much the hatred of my spirit / For I am sick when I do look on thee" (II.i.215-216). Not only does he threaten her with physical violence, he threatens to rape her as we see in his next lines:
You do impeach your modesty too much
To leave the city and commit yourself
Into the hands of one that loves you not;
To trust the opportunity of night,
With the rich worth of your virginity. (218-223)
In great contrast to Demetrius, Lysander is portrayed as sensitive and respectful, especially towards Hermia. We see him being sensitive when, after she is warned by Theseus of her possible sentences, Lysander sees how distraught and frightened Hermia is and sensitively remarks, "How now, my love! Why is your cheek so pale? / How chance the roses there do fade so fast?" (I.i.130-131). When the couple is in the woods escaping Athens together, similar to Demetrius, Lysander expresses his sexual desires as well; however, in great contrast to Demetrius, he does so in a way that shows Hermia respect and preserves her honor. We see Lysander expressing his sexual desires when he suggests that they rest for the night and that Hermia should sleep with him, as we see in the lines, "One turf shall serve as pillow for us both; / One heart, one bed, two bosoms. and one troth" (II.ii.42-43). However, like a virtuous maiden, Hermia strives to preserve her honor and tells him to sleep elsewhere, which "Becomes a virtuous bachelor and a maid" (60). While he protests at first, respecting her, he gladly relents, saying, "Amen, amen, to that fair prayer say I" (63).
Hence, we see that one major difference between Demetrius and Lysander is that Demetrius is characterized as an aggressive bully, while Lysander is sensitive and respectful.