Well i think they both died. Rosette was at her limit when they met in the church and Chrno didn't have his horns anymore (probabily because of the batte with aion).
I find it a little sad. I would've liked it if one of them survived in the end so that the other wouldn't be forgotten
I Rosette was the only one who died in the manga. Because who else would be the one who put flowers in her grave (when Satella found them)? The grand son of Joshua & Azumaria said it hapened every year, which means that every year Chrono comes to her grave & put flowers their for her
I think*
SPOILER!!!!
What happened to Chrno? If he also died it would be soo touching, if Chrno and Rosette got buried together.