I'm playing LMoP at the moment as a player and I'm trying to see reasons why a player would choose Unseen Servant over Find Familiar. Related question – what makes Unseen Servant worth taking instead of Mage Hand?
Here's a small comparison table I've created when I was trying to figure it out.
|Mage Hand||Unseen Servant||Find Familiar|
|Level||cantrip||1 level||1 level|
|Casting time||action||action/10 minutes||1 hour|
|Casting cost||0 gp||0 gp||10 gp|
|Duration||1 minute||1 hour||until killed/dispelled|
|Command time||action||bonus action||free action|
|Carrying capacity||10 lbs||60 lbs||90 lbs (depends on Str)|
|Movement||30 ft||15 ft||60 ft|
|Drop items in combat||yes||yes||yes|
The spells all have different use cases:
Mage Hand is for performing a simple task at a distance:
This can be useful for things such as distracting enemies out of combat or for adding flair to your character ("my wizard is too fancy to pour his own wine"). Note that you need to use an entire action to control the hand, suggesting that it takes up some of the users focus to perform the action.
Advantage over the other spells: The mage hand can't take damage allowing it to perform dangerous tasks such as picking up an item from a pool of acid or attempting to activate a trap (would damage and dispel the servant and hurt and possibly dispel the familiar).
Unseen Servant is for more advanced tasks and several tasks at once:
The unseen servant can be given a more advanced command which it will then execute, allowing the caster to focus on other things. You could probably fold your laundry with Mage Hand, but it would be just as boring and time consuming as folding it with your own hands (or even more so since you'd have to do it single-handedly).
Advantage over the other spells: As there are no restrictions for how many servants you can have at once, you can essentially let them perform all your partys rest activities while leaving you free to rest or meditate or whatever.
Note: The unseen servant is also created "on the ground" and can do "simple tasks that a human servant could do" suggesting it can't fly or perform actions in the air (although not specified per se).
Find Familiar can perform different tasks depending on what form it has and also has uses in combat. You could change your cat familiar into a raven to attach a rope to the top of a wall, but do you want to spend 1hr and 10gp to cast the spell again, or do you use mage hand? Do you want an owl to fold your laundry or do you cast unseen servant?
Advantage over the other spells: As showcased in your table the familiar has a lot of advantages over the other two spells (duration, speed, carry capacity etc), but some of the things that really make it stand out is the ability to communicate with it, that it can deliver touch-range spells for you and that you can share its senses.
Note: As mentioned in comments; remember that the familiar has all the mental statistics of the animal it resembles. Your DM might rule that the telepathic communication with a 1 Int crab is mostly gibberish relating to fish.