Is there a benefit to a savory breakfast over a sweet breakfast even if both versions are healthy?

I prefer savory breakfast , I am not big sugar eater and I have noticed that sweet breakfast trigger cravings all day. I prefer to have a little sweet in the afternoon after lunch.

Yes. It's better not to raise your blood sugar so high in the morning (or anytime really). So, try to keep the sugar content lower…even if it's from natural forms of sugar (i.e. fruit, etc.)
Balance sugar with protein to keep your blood sugar more level.

I think it depends on the person, some people dont enjoy sweet things as much as others. I dont think there is a benefit to either because they are both healthy.

I prefer a savory breakfast. I want to lose weight so I dont want to eat so much sugar. But not fat either (for example cheese or oils with bread). I just feel myself more energized with a savory breakfast and also more full for a longer time.