Whether specific foods are actually healthier is debatable, but when it comes to the abundance of nutrients such as lycopene, conclusive measurements can be made.
Cooked sauce also had the effect of transforming the lycopene present in the tomato, which helped preserve its integrity through the digestive process, allowing more of this important antioxidant to be absorbed. Noted Heredia, "[W]e found serving meals rich in probiotics with fried tomato sauce boosts its probiotic effect, as well as causing a progressive isomerization of the lycopene of the tomato, from form cis to trans throughout digestion, which positively results in an increased final bioaccessibility of this carotenoid."
— Cooking Tomatoes Increases Lycopene and Beneficial Bacteria
Other studies have shown that how food is cooked also has a significant effect:
We conclude that the addition of olive oil to diced tomatoes during cooking greatly increases the absorption of lycopene. The results highlight the importance of cuisine (i.e how a food is prepared and consumed) in determining the bioavailability of dietary carotenoids such as lycopene.
— (Increases in plasma lycopene concentration after consumption of tomatoes cooked with olive oil — US National Library of Medicine, National Institutes of Health)
I.e. cooking tomatoes helps to release greater quantities of lycopene into the food, and combining it with olive oil helps to increase the amount absorbed during digestion.
So, if by "healthier" you mean do cooked tomatoes provide more available lycopene (and other nutrients) than fresh tomatoes?, the answer is yes.