The short answer
If you are staying in one seat near an outlet with your own cable and adapter, use the outlet. If you are moving, or the outlet is not where you are sitting, rent.
Side by side
Price: an outlet is free; a rental is $2 per 30 minutes, capped at $12 per 24-hour day. What you bring: an outlet needs your own cable and adapter; a rental has built-in cables. Where your phone is: plugged into the wall versus in your pocket. Where you are: next to the socket versus wherever you want to be. Returns: none for an outlet; any Juiceboxx station for a rental.
What an outlet really costs
No money, but time and freedom. Your phone stays plugged in where the socket is, and so do you. You also need your own cable and adapter, and the outlet has to be free.
What a rental costs
A Juiceboxx rental is $2 for each 30 minutes, capped at $12 per 24-hour day. A quick top-up costs a couple of dollars. Even a long evening stops at the daily cap. Your phone charges in your pocket while you keep going.
When the outlet is the better choice
Overnight in a hotel room, at your desk, or anywhere you will stay put for a few hours. That is what outlets are for.
When the rental is the point
When the group is moving to the next spot, when the only outlet is across the room, or when you left your cable at home. You can rent at one station and return at another. See the power bank comparison and the station finder.
The hidden costs of the outlet
Outlets in public places are often taken, broken, or in awkward spots behind furniture. Leaving your phone plugged in unattended means trusting strangers with it. And standing next to an outlet means you are not with your group. None of that shows up on a bill, but it is real.
A quick way to decide
Ask two questions. Will you stay within reach of the outlet for the next hour? Do you have your own cable and adapter? If both answers are yes, use the outlet. If either is no, a rental is the better choice, and it will usually cost less than a drink.
How long a top-up takes
Charging speed depends on the phone, the cable, the adapter or power bank, and what the phone is doing at the time. A phone with the screen off charges faster than one running a game or navigation, whichever source you use. For a night out, the question is rarely how fast. It is whether you can keep using the phone while it charges.
The limit of both
Neither option fixes a damaged charging port, and both need your phone to have enough charge to get started. Rent while you still have a little battery left.