It can never be as simple as "Homura and Madoka are happy", can it?

Nope! No it cannot.

One interpretation of the series—with tragic implications—is that Madoka and Homuras' wishes mutually exclude each other by definition. Original-timeline Homura doesn't just wish to protect Madoka; she wishes to protect Madoka instead of Madoka protecting her. Later, penultimate-timeline Madoka wishes to erase all witches with her own hands.

Homura's wish explicitly precludes the existence of any iteration of Mahou Shoujo Madoka, to say nothing of "Godoka". Even without the climax of Walpurgisnacht, Mahou Shoujo Madoka would have become a witch in every timeline without fail, so the only acceptable timeline for Homura was one in which Madoka didn't contract. But on top of that, Homura is incapable of protecting non-magical Madoka in any timeline—we know from the series finale that the purity of her Soul Gem is a hard limit on the number of times she can loop. Bill Murray could loop thousands and thousands of times because there was no danger of him losing hope and turning into a witch (or groundhog), even via suicide.

So basically, Homura is stuck in a tragic catch-22. The final timeline was an uneasy and precarious balance because Homura had lost all memories of her driving need to protect Madoka, but once those floodgates open in Rebellion...

On the other hand, penultimate-timeline Madoka's wish doesn't preclude Mahou Shoujo Homura (and arguably encourages a healthy system of magical girls to keep the peace throughout history). However, a reality in which Madoka is a total bystander—which Homura fabricates at the end of Rebellion—would be utterly unacceptable to Madoka if she were to remember (or when, inevitably, she does remember) her wish.

So. That's what frames Madoka and Homura as "enemies." Their wishes are in direct opposition to each other which brings them, as mahou shoujo, in direction opposition to each other. At any time or in any timeline in which Madoka and Homura have full memories of their wishes, they will be in conflict with each other, and they won't be happy. And that's tragic.