It depends on the capacitor and the radio as far as how long will it last. Coupled with are you taking a solar panel or other means to charge it.
They are big in the CB big amp community right now because what took a pickup trucks full bed for storage capacity is not in something the size of a large car battery.
I have seen videos of guys keying up 1000 watt plus amplifiers for more than a minute with a single super cap and only drain it 10 percent.
But you still need to do the math to figure out how long.
What is the load, are you running 100 watts, QRP, or something in between?
Are you trying to contest with it or spin up communications at some super rare grid square that is going to have you making contact after contact or are you just gonna rag chew for a bit and call it good?
The way to figure all this out is get the load current at idle, receiving. Convert that to watts.
Get the load current transmitting, and again convert that to watts.
Take those numbers and figure out how much you are going to be doing of both in either amp hours or watt hours and choose a battery or capacitor with the capacity that your math says you will need.
Obviously a large super cap is going to be heavy and reasonably big. Leaving little room in your pack for much else if you are planning to activate a rare grid square and be on the radio a lot.
A better antenna is always a good choice over more power. And something people seem to forget is that a beam can be constructed out of wire and hung from trees or what every natural vertical real estate that's there. If you pick a specific band, and design your antenna for that band, you can see 6 or maybe 9 db of directional gain. And if you put that up against the side of the mountain using it as the reflector you will see higher directional gain numbers. Gain and 10 watts is better than 100 watts and a crap antenna. gain is reciprocal. Meaning you get gain on receive as well as transmit. Some short single element antenna with a tuner because it's not resonant will not hear near as good and will not talk near as far. SO bare that in mind too.
Not sure what you are planning, so that should give you enough information to start putting things together.