One of the big things divides Kagome and Kikyo, particularly after Kikyo's death, is Kagome's selflessness. She goes out of her way to help those that are in distress, even when she might benefit from letting them die instead- particularly in the scene where Kagome jumps into the pond to purify Kikyo's spirit. She was never thanked for it, and she didn't gain from it, but she did it anyways.
The thing they share is their courage- even when faced with adversity, you don't see Kikyo and Kagome backing down- and if Kikyo does, it's more of an "I don't wanna do it" thing than it is "I'm too afraid."
Kikyo is dignified and introspective, whereas Kagome is gregarious and spirited. Inspecting Inuyasha's demeanor, he is the kind of person that likes to portray himself as careless and tough, but has a gentle heart (like when Kagome says "I hate you" after saving Kikyo's life when Naraku's evil energy had begun to taint her, and Inuyasha admits that it hurt him, whereas Kagome barely remembered saying it) which he reveals through his willingness to step up to the plate and defend others.
The love Inuyasha and Kikyo was brief and hot-blooded, sweet and transient like daylight in an Arctic winter. On the other hand, the bond he built with Kagome was something they built via adversity, blood and tears shed together, providing and caring for one another, and TIME.
Ultimately, while Kikyo before her death was a lively person, post-mortem she is only quite literally a shell of herself, as she only has a tiny fragment of her and Kagome's shared soul stored inside of a clay body (from when the witch brought her back from the dead and Kagome's body absorbed most of the soul back into herself).
It's notable, however, that Inuyasha was with Kikyo out of choice, and went back to her out of choice, as when he followed her tree to tree, spoke with her, and agreed voluntarily to meet her at the Tree of Ages to give up his demon half. He has no choice where it comes to Kagome- she was thrust into his life and even uses the Beads of Subjugation around his neck for vengeful and immature purposes and to restrain his wild nature- they were something that Kikyo ultimately decided she didn't need for him.
Inuyasha and Kikyo were two lonely souls, Kikyo out of the solemn duty to the Shikon Jewel, and Inuyasha because neither the community of demons nor humans would accept him as one of their own. They found kinship, community, and companionship in each other.
Kagome accepted Inuyasha unconditionally. She shows open affection and worry for him, like when she ran toward him in the episode where Inuyasha plummeted over the cliff and she was unsure if he'd been able to survive the fall. The experiences they have shared are numerous, diverse, and impactful- the battles they've been in, the lands they've traveled, and the arguments they've had and resolved. You guys have seen it.
The whole love triangle thing makes me mad sometimes, too.