The Flagship Lounge will have better food/beverage service as well as more personalized service due to the higher ratio of attendants to passengers.
In the Boston AC, there's the bar, and coffee. Food is limited to some crackers. In the Flagship Lounge, it's an open bar and there's a nice selection of breakfast foods. Also more selectoins in magazines and newspapers.
In the AC, you just have to clear the front desk and then you're left alone. You have to keep an eye on the board or an ear on the PA announcements to know when your flight is boarding. In the Flagship Lounge, they'll take down your name and flight number and come around to remind you in person that your flight is boarding. No rude annoucements, and no need to keep an eye on the departure screen.
So it's like the difference in service between Int'l Business and Int'l First. Much the same, just more refined.