Ships & Modules

Don't use any race's battleship for Vanguards. You want to use Cruiser-sized ships for them, for tracking and for tanking. The only exceptions are pirate-faction pimp mobiles, like the Vindicator and Nightmare.

Battleships are not very useful for PVE right now, given the greater effective DPS numbers you can apply across various target types with a Drake, Nighthawk or Tengu. So far as Vanguards go, I don't know how you kids do it wherever you're from but in goon space we run armor fleets for Vanguards; so, we use Hurricanes for newbies, with preference on Legion > Guardian > Zealot > Loki > Hurricane. An ideal Vanguard fleet has 3 Guardians, 6 Legions, and 1 Loki.

Agreed with the lack of useful caldari BS for incursions, because large missiles suck and the rohk doesn't have any damage bonuses which makes it very lackluster. If you want one ship that can effectively run both vanguards and lvl 4's, you want a tengu, because if you are putting on 2 rigor and 1 flare rig, you can keep that rig setup for both lvl 4's and for vans. The subsystems are also mostly the same, and you use 4 damage mods for each. Example fits:

Note, ment to be run with fleet booster, if there isn't one available drop a painter for an invuln, and if you are feeling too squishy then maybe a second mid for an extender.
[Tengu, Incursion Vanguard]
Caldari Navy Ballistic Control System
Caldari Navy Ballistic Control System
Caldari Navy Ballistic Control System
Caldari Navy Ballistic Control System

Photon Scattering Field II
Photon Scattering Field II
Explosion Dampening Field II
Phased Weapon Navigation Array Generation Extron
Phased Weapon Navigation Array Generation Extron
Federation Navy Stasis Webifier

Heavy Missile Launcher II, Scourge Fury Heavy Missile
Heavy Missile Launcher II, Scourge Fury Heavy Missile
Heavy Missile Launcher II, Scourge Fury Heavy Missile
Heavy Missile Launcher II, Scourge Fury Heavy Missile
Heavy Missile Launcher II, Scourge Fury Heavy Missile
Heavy Missile Launcher II, Scourge Fury Heavy Missile

Medium Warhead Rigor Catalyst II
Medium Warhead Rigor Catalyst II
Medium Warhead Flare Catalyst II

Tengu Defensive - Supplemental Screening
Tengu Electronics - Dissolution Sequencer
Tengu Engineering - Augmented Capacitor Reservoir
Tengu Offensive - Accelerated Ejection Bay
Tengu Propulsion - Intercalated Nanofibers

for lvl 4's, you generally go with this. Note, you do have to swap a subsystem, but that isn't a big deal, and you can pimp the tank a bit if you need to.
[Tengu, Heavy]
Caldari Navy Ballistic Control System
Caldari Navy Ballistic Control System
Caldari Navy Ballistic Control System
Caldari Navy Ballistic Control System

Medium Shield Booster II
Heat Dissipation Field II
Heat Dissipation Field II
Ballistic Deflection Field II
Ballistic Deflection Field II
Cap Recharger II

Heavy Missile Launcher II, Scourge Heavy Missile
Heavy Missile Launcher II, Scourge Heavy Missile
Heavy Missile Launcher II, Scourge Heavy Missile
Heavy Missile Launcher II, Scourge Heavy Missile
Heavy Missile Launcher II, Scourge Heavy Missile
Heavy Missile Launcher II, Scourge Heavy Missile

Medium Warhead Flare Catalyst II
Medium Warhead Rigor Catalyst II
Medium Warhead Rigor Catalyst II

Tengu Defensive - Amplification Node
Tengu Electronics - Dissolution Sequencer
Tengu Engineering - Augmented Capacitor Reservoir
Tengu Offensive - Accelerated Ejection Bay
Tengu Propulsion - Intercalated Nanofibers

-Arazel

Assuming you're asking "why do most highsec incursion runners favour shield-tanked battleships?" and not "why are you posting shield-tanked Tengu fits?", the answer is that shield fleets of moderately pimped turret BS that are fit for minimum tank and maximum DPS/utility (read: plenty of webs and sensor boosters) do 80-100% more damage than AHAC-type T3s and don't have issues applying it quickly to the NPCs found in VGs. Also, most highsec carebears/carebear alts are trained for shield tanking ships.

Your T3s might have an edge in NCOs, I'll give you that. However, I daresay part of the reason you favour cruiser-sized ships is that you can pack lots of them into a single carrier when the next incursion spawns rather than having to make several jumps to ferry peoples' battleships around.

Thank you both for those quick and informative responses! I wish there was more for me to say here, but I really am ignorant of the game mechanics involved here and pretty much just need to take your word that you know what you're saying. Both of your points make sense, and the conclusions you draw seem reasonable from my perspective. Thanks again! I was always curious.

Why not just get two ships then?

buy 2 different ships.

Tengu outperforms the Nighthawk handily for sub-BS platforms. It also outdpses a cruise raven when you dont factor in the raven's drones (which wont add that much dps in an incursion). the tengu will also have better damage projection on the cruisers. The raven has more ehp, but the tengus smaller sig means it will take less damage overall and be easier on the logi.