It’s recommended (mustahab) for men to cover their head, especially in prayer. So yes it is better. Socially the dress of men has changed (influenced mainly by western culture) and so most men today don’t cover their head anymore.
And yes men should veil themselves too. It’s a sign of respect, modesty and being appropriate.
By the way, while praying at home, you can wear the Abaya and cover your head during prayer. That way the reward for your prayer will increase Insha’Allah.