I will quote Cap because the list is quite handy.
(...)
Let's compare:
Weapon attacks, dual wielding style: 2d8+10 damage
Weapon attacks, greatweapon style: 2d12+10 damage but no assured bonus action, so only 1d12+5 damage for comparison purposes.
Acid Splash: 2d6 to two creatures is pretty nice, but they get a Dex save to negate and must stand next to each other.
This could be useful in some circumstances. The Dex save was pointed out as a negative feature, but it could be positive also, as you don't need to roll to hit, and some monsters do have good AC but crappy saves. Anyhow, maybe GFB is a more consistent option for a similar scenario.
Poison Spray: 2d12 damage, Con save to negate, poison resistance/immunity is common
Again, this could be good or bad. It is not that difficult to figure out whether a monster has good Con saves (big burly brutes) or poison resistance/immunity (most often poisonous monsters themselves). 2d12 is definitely a nice damage.
Shocking Grasp: 2d8 though with advantage (assuming a foe in metal armor), and foe can't take his reaction.
The secondary effect can be quite handy if you want to reposition yourself or give an ally an easy escape.
My take is that weapon attacks are more reliable, in several ways. Hitting AC is easier at mid-levels than getting in a Con or Dex save. Acid Splash and Poison Spray are circumstancial, so you need more than one such trick.
And that is what may limit the use of warcaster with only the PHB cantrips, as all the eldritch knight gets a limited list of cantrips (as most classes do), and as pointed out, their use is circumstantial, so to make its use more frequent, you would need a large selection of cantrips.
I would say Shocking Grasp is the best contender, assuming you use it where you gain advantage. Losing ability bonus damage is a big negative, though.
I'm sure there are splatbook cantrips that are better. In fact I hope so - or War Magic is niche at best.
Yes, SCAG makes a huge difference here. Now, from levels 7 to ten, and later from levels 17 to 19 the cantrip (BB or GFB) plus bonus action attack (assuming non-dual wielder) is usually the dominating tactic, and can even be the best choice circumstantially from levels 11 to 16. Sword and board warcaster types are probably the ones that favor the most of its use, as great weapon users with GWM or PAM may have a competing option for their bonus action.
But if you don't use those sources, I'd say: stick to doing weapon damage.
Good thing there are these sources. I felt the same as [MENTION=12731]CapnZapp[/MENTION] the first time I saw this feature (niche), and felt like the SCAG cantrips came to address this.