Witch Bolt is borderline useless
- It requires concentration
- Its range is so short that enemies can leave it in a single turn unless someone reduces their speed.
- The fact that it ends if you don't continue to use your action on it makes it very inflexible.
- The arc of lightning makes you an obvious target to all enemies.
- Even if used on the first turn of combat, many fights will end well before the full duration has expired.
- Most importantly, its damage is so low that there's always a better option.
For an Eldritch Knight:
Witch Bolt deals an average of 6.5 damage per round. A single longsword attack deals the same average damage with a Strength modifier of only +2.
Sure, the weapon attacks will miss X% of turns, but Witch Bolt will also miss X% of the time or less (ideally your weapon attack bonus is at least as high as your spell attack bonus.) What's more, Eldritch Knights gain spell slots very slowly (3 times as slow as spellcasters) so wasting a slot is a big problem.
Let's consider a 13 AC enemy (the expected AC for a CR 0 to 3 monster) and an Eldritch Knight with +3 Strength, +3 Intelligence wielding a longsword one-handed. With an attack bonus of +5, the Eldritch Knight's attacks will hit 65% of the time. Finally, let's assume you have 4 turns to deal damage.
Witch Bolt average damage over 4 turns:
|0.35 × 0.65
|0.35² × 0.65
|0.35³ × 0.65
If you do the math, Witch Bolt has an expected damage of 22.55 over 4 rounds, and has an average cost of 1.5 spell slots. (Or put differently, about 1/3 of the time you have to pay 2 slots and lose 1 turn's worth of damage.)
On the other hand Magic Missile can't miss and deals an average of 10.5 damage, and three longsword attacks will add an average of 7.5 * 3 * 0.65 = 14.625 for a total of 25.125 over 4 rounds, and only costs 1 spell slot. So Magic Missile is already a better option even without taking critical hits into account. (Any of the weapon attacks can score a critical, but the following turns of Witch Bolt can't.)
Burning Hands would also do the same average damage as Magic Missile if the target fails its save, and you still get half damage if it succeeds. If you can hit 2 creatures, it's a no-brainer.
And these are very conservative numbers for a Fighter! Any Fighting Style other than Armor or Protection would increase the damage further. If we're talking about a variant human with Polearm Master or Crossbow Expert, Witch Bolt doesn't stand a chance.
If you use True Strike beforehand, the damage looks like this:
|0.1225 × 0.8775 × 6.5
There's only two outcomes since you're using 2 turns at a time. Anyways, the math works out to an expected 17.8 damage over 4 turns at an average cost of 1.14 slots. Less likely to be wasteful, but also less damage.
Against a very high AC enemy Witch Bolt might seem appealing since the damage on subsequent rounds is guaranteed, but your chance of missing and wasting the turn are also much higher. Enemies with high AC - especially at lower CRs - are usually wearing medium or heavy armor and don't have good Dexterity saving throws, so you're much better off relying on Magic Missile or Burning Hands.
In short, Witch Bolt is never a good option for an Eldritch Knight.
For a Wizard/Sorcerer: While they'll deal less damage with their cantrips than an Eldritch Knight does with weapon attacks, they get much better access to concentration spells (e.g. Sleep, Grease) and the spell slots to make use of them. At level 3, Flaming Sphere or Scorching Ray will kill things much faster, and Web becomes another candidate for concentration. At level 5 cantrips go up in power and you get very similar numbers to the Eldritch Knight's.
For a Warlock:
Witch Bolt is worse than Hex + Eldritch Blast in every practical situation. 1d10 + 1d6 add up to 9 damage per round on average. That's 23.4 damage over 4 rounds once you take the 65% hit rate into account, and costs 1 slot since Hex has no save.
On top of that Hex's ability to impose disadvantage on ability checks can help you or other party members hide by giving the enemy disadvantage on Perception checks, or help them shove or grapple that enemy by hurting their Athletics or Acrobatics.
The final nail in the coffin is that Witch Bolt is only good for one creature; Hex can easily be applied to 2 creatures or more, and in a dungeon can potentially last until your next short rest. The extra range on Hex and Eldritch Blast help make this possible since you'll be out of attack range more often and thus make make less concentration saves.