I mean that depends entirely on what you as the player want to use the vessel for, and who you ask as per usual the term “Battlecruiser” especially in sci-fi or fantasy has been stretched quite wide & thin in contrary to it’s IRL usage.
In our Aurora game that me and my 2 friends run (5 years per person), we’re all military autists and one particularly is a heavy navy autist. Our navy is using similar tonnage as 1940 ish period, using this array
Hull Classes - V3
70k - 100k = BS
50k - 70k = DN
30k - 50k = BB
20k - 30k = BC
15k - 20k = CA
10k - 15k = CL
5K - 10k = DD
0.5k - 5k = FAC,FF, Corv, etc
0k - 0.5k = Fighter, Bomber, etc
We put the classification more on tonnage & speed rather than purpose, as Aurora makes it difficult in that manner. So a Battlecruiser design we have is this, 75years into our game.
Oh also, we’ve made a rule to NOT use shields, so it’s Armour or nothing. Gotta pay good for good armour 
Spatha Block 4 class Battlecruiser 27,926 tons 797 Crew 5,251.2 BP TCS 559 TH 3,938 EM 0
7049 km/s Armour 12-81 Shields 0-0 HTK 155 Sensors 1/1/0/0 DCR 22-7 PPV 129.92
Maint Life 1.35 Years MSP 2,410 AFR 520% IFR 7.2% 1YR 1,423 5YR 21,345 Max Repair 656.3 MSP
Troop Capacity 300 tons Boarding Capable Magazine 200 / 150 Cryogenic Berths 800
Captain Control Rating 5 BRG AUX ENG CIC FLG
Intended Deployment Time: 6 months Morale Check Required
ID-3000/175-1312EP (3) Power 3937.5 Fuel Use 115.78% Signature 1312.5 Explosion 17%
Fuel Capacity 1,500,000 Litres Range 8.3 billion km (13 days at full power)
250mm(UL)-640k/ROF30 (1) Range 256,000km TS: 7,049 km/s Power 16-3 RM 40,000 km ROF 30
Single 200mm(UL)-400k/ROF30 Turret (1x1) Range 256,000km TS: 20000 km/s Power 10-3 RM 40,000 km ROF 20
PB-4/200k (10) Range 200,000km TS: 7,049 km/s Power 10-3 ROF 20
Quad Turret - GC-30k/50-(17%) (4x12) Range 30,000km TS: 20000 km/s Power 0-0 RM 30,000 km ROF 5
BFC(MW)-300/256k-9Kps (1) Max Range: 256,000 km TS: 9,000 km/s ECCM-1 96 92 88 84 80 77 73 69 65 61
BFC(MW-PD)-300/192k-12Kps (1) Max Range: 192,000 km TS: 12,000 km/s ECCM-1 95 90 84 79 74 69 64 58 53 48
SFR-95/16.76 (3) Total Power Output 50.3 Exp 5%
DML-10 (15) Decoy Size: 10 Hangar Reload 158 minutes MF Reload 26 hours
BL-02 (100) Missile Size: 2 Hangar Reload 70 minutes MF Reload 11 hours
MFC-300/MSL-3.2M (1) Range 35.8m km Resolution 1 ECCM-1
M10 Decoy Missile (15) Signature: 2000 tons ECM-0 Size: 10
M2A3 "Space Cobra" AMM (100) Speed: 37,500 km/s End: 0.8m Range: 1.8m km WH: 1 Size: 2 TH: 125/75/37
AS-25/10kT-30M (1) GPS 2100 Range 30.2m km Resolution 200
AS-100/MSL-930K (1) GPS 42 Range 10.3m km MCR 930.8k km Resolution 1
EM-10/8 (1) Sensitivity 1.6 Detect Sig Strength 1000: 10m km
TH-10/8 (1) Sensitivity 1.6 Detect Sig Strength 1000: 10m km
Electronic Warfare Jammers: Sensor 1 Fire Control 2 Missile 2
Ground Forces
1x Space H.Marines - 2348
2x Space Marines - 2348
Missile to hit chances are vs targets moving at 3000 km/s, 5000 km/s and 10,000 km/s
This design is classed as a Military Vessel for maintenance purposes
This design is classed as a Warship for auto-assignment purposes
For comparison, this is out Battleship.
We Came. We Stomped. We Laughed. III class Battleship 49,941 tons 1,072 Crew 8,822.5 BP TCS 999 TH 4,500 EM 0
4505 km/s Armour 25-120 Shields 0-0 HTK 285 Sensors 1/1/0/0 DCR 38-7 PPV 267.8
Maint Life 1.88 Years MSP 4,591 AFR 713% IFR 9.9% 1YR 1,658 5YR 24,870 Max Repair 750 MSP
Troop Capacity 500 tons Boarding Capable Magazine 200 / 250 Cryogenic Berths 1,000
Captain Control Rating 5 BRG AUX ENG CIC FLG
Intended Deployment Time: 6 months Morale Check Required
ID-3000/200-1500EP (3) Power 4500 Fuel Use 161.66% Signature 1500 Explosion 20%
Fuel Capacity 4,000,000 Litres Range 8.9 billion km (22 days at full power)
250mm(UL)-640k/ROF30 (1) Range 256,000km TS: 4,505 km/s Power 16-3 RM 40,000 km ROF 30
Triple 200mm(UL)-400k/ROF30 Turret (5x3) Range 256,000km TS: 12000 km/s Power 30-9 RM 40,000 km ROF 20
Quad Turret - GC-30k/50-(17%) (20x12) Range 30,000km TS: 20000 km/s Power 0-0 RM 30,000 km ROF 5
BFC(MW-PD)-300/192k-12Kps (1) Max Range: 192,000 km TS: 12,000 km/s ECCM-1 95 90 84 79 74 69 64 58 53 48
BFC(MW)-300/256k-9Kps (1) Max Range: 256,000 km TS: 9,000 km/s ECCM-1 96 92 88 84 80 77 73 69 65 61
SFR-95/16.76 (4) Total Power Output 67 Exp 5%
DML-10 (25) Decoy Size: 10 Hangar Reload 158 minutes MF Reload 26 hours
BL-02 (100) Missile Size: 2 Hangar Reload 70 minutes MF Reload 11 hours
MFC-50/MSL-1.3M (1) Range 14.6m km Resolution 1 ECCM-1
M10 Decoy Missile (25) Signature: 2000 tons ECM-0 Size: 10
M2A3 "Space Cobra" AMM (100) Speed: 37,500 km/s End: 0.8m Range: 1.8m km WH: 1 Size: 2 TH: 125/75/37
AS-300/MSL-1.6M (1) GPS 126 Range 17.9m km MCR 1.6m km Resolution 1
AS-300/10kT-104M (1) GPS 25200 Range 104.8m km Resolution 200
TH-10/8 (1) Sensitivity 1.6 Detect Sig Strength 1000: 10m km
EM-10/8 (1) Sensitivity 1.6 Detect Sig Strength 1000: 10m km
Electronic Warfare Jammers: Sensor 1 Fire Control 2 Missile 2
Ground Forces
5x Space H.Marines - 2348
Missile to hit chances are vs targets moving at 3000 km/s, 5000 km/s and 10,000 km/s
This design is classed as a Military Vessel for maintenance purposes
This design is classed as a Warship for auto-assignment purposes
As you can notice, our Battlecruiser is smaller by 20k tons, but has heavy armaments in terms of a interchangeable Fixed Laser OR Particle Lance, along with fixed Particlebeams & AA, less armour but speedy. While the Battleship is s heavy uparmoured ship with large turrets, heavy AA and a fixed Laser. Both also have a wide array of missiles mostly AMMs.
Task we use the BC for is escorting the BB along with a large complement of DDs, CLs & CAs. When encountering threats, if a DD, CL or particularly CAs can’t be used the BC is sent in to recon and chase.
When in a fleet battle, when or if the enemy fleet starts fleeing, the BC is sent to chase with a large escort force (consisting of DDs and CLs), to catch up to either send boarding marines, completely wreck the fleeing ships or chase them until they encounter the JP.
In contrary to BCs, the BB’s main purpose is to be a anchor of threat, particularly against missile heavy opponents, OR guarding JPs with their very heavy armour able to slug it out for hours against any hostile threat.
Is this a game optimal playstyle? Hell no, we enjoy recreating IRL navy standards from 1910 → 1990, with large supplement of Destroyers, Light Cruisers and more.
But it is certainly one example of a navy doctrine me and my friends use 