Let's not kid ourselves, the Defiant was right there and she was designed to fight the Borg.
While the
Defiant was designed to fight the Borg, she wasn't intended to solo a cube. She was supposed to be part of a squadron of Borg-Busters. While she's powerful for her size she's also
tiny. The
Defiant struggled going 1-to-1 against a refit
Excelsior-class and was left adrift and powerless after the Battle of Sector 001 despite there being many other ships there – indeed she only survived at all because of the timely intervention of the
Enterprise-E. We hardly ever see her take on a capital ship directly during the Dominion War. The only thing she really has over a
Galaxy-class is manoeuvrability – in a straight see-who-hits-hardest competition for raw firepower in absolute terms my money's on the
Galaxy-class.
If they were really going for the most well-armed ship in the museum they should have picked the
Akira-class USS
Sentinel, But based on what Geordi says she's not fully operational. Besides, some of Picard's crew haven't been on starships in decades – how up-to-date do you think they are on
Defiant-class or
Akira-class operations? Better stick with the ship they know top-to-bottom and upside-down. To quote Riker in "The Best of Both Worlds":
"But this is not the time for change. I need you all where you are, where Captain Picard always relied on you."
And had a cloaking device.
The
Defiant with the cloaking device was the original, NX-74205, destroyed in DS9: "The Changing Face of Evil". The cloak was unique to the original
Defiant and is not a standard feature of the class. The second
Defiant, the rechristened
Sao Paulo NCC-75633 which is the one in the Starfleet Museum, did not have a cloaking device.