A more realistic one would be USS Texas and Bismark. Apparently Texas was on a neutrality patrol in the Denmark strait about 12 hours before Hood and Prince of Wales had their fateful encounter. I could see a spooked Bismark opening fire on a "RN Battleship", how long would Texas last?
Not very. It does have torpedo bulges, that might help some against below waterline hits.
This looks like a mismatch. The New York's out ranged by 24 km and 9 knots slower. Both ships have radar.
New York
Main Guns
10 × 14 in (356 mm)/45 caliber guns
Effective firing range 12 km (7.4 mi) at 7.4° elevation
Maximum firing range 21 km (13.1 mi) at 15° elevation
Armor
Belt: 6–12 in (152–305 mm)
Bulkheads: 10 to 11 in (254 to 279 mm)
Barbettes: 5–12 in (127–305 mm)
Turrets: 14 in (356 mm) (face)
Decks: 1.5–3 in (38–76 mm)
Conning tower: 12 in
Speed 21 knots
Bismark
Armament
8 × 38 cm (15 in) SK C/34 (4 × 2)
Effective firing range 36.5 km (22.7 mi) with 800 kg (1,800 lb) shell at 30° elev.
Maximum firing range 55.7 km (34.6 mi) with 495 kg (1,091 lb) shell at 30° elev.
Armour
Belt: 320 mm (12.6 in)
Turrets: 360 mm (14.2 in)
Main deck: 100–120 mm (3.9–4.7 in)
Speed 30 knots