Browning better engineered? Don't think so. While Browning is surely a workhorse and super reliable guns, they are not the "be all end all" of shotguns. Before I go any farther, you should buy the the gun that fits you best.
Browning is the consumate copier of the shotgun world and one would be hard pressed to find a modern gun with the Browning name on it. The Cynegy is a copy type of the Fabarm Axis that was introduced 5 years ahead of the Browning version & this year The introduced a stylized semi auto (Maxus) that internally is very similar to Fabarm Semi's.
The Savage Milano, I have read, is made by Isidore Rizzini (FAIR) . A well respected Italian gunmaker who also produce Verona & Cortona for the US market. I own several several FAIR guns and feel the surpass Browning for fit, finish overall quality. The Milano is an entry level gun very similar to the Premier FAIR without the bells and whistles of the Browning.
Again your choice of shotgun should hinge on two things -- fit & fit. First is how the particular fits you and then how it fits your budget. Both of these guns are well engineered and both will give you years of reliable shooting.
Cheers/Luck!