This question comes up in almost every first conversation, usually phrased apologetically, as though there's a right answer I'm going to be annoyed about.
There isn't. They do genuinely different things, and which one matters more depends on what you're like.
What photographs do
Photographs get looked at. That sounds obvious, but it's the whole argument.
A photograph sits on a shelf, goes in a frame, gets sent to your grandmother, becomes the picture on the wall for the next thirty years. You'll see your wedding photographs thousands of times. They're woven into the house.
They're also easier to share, easier to print, and they don't ask anything of the person looking. Nobody has to set aside an hour.
What a film does
A film gives you the things a photograph structurally cannot hold: voices, and time.
Your dad's speech. The exact way your friend's voice cracked. The registrar's phrasing. The song that was actually playing when you walked in, rather than the one you thought was playing. The five seconds before the first kiss, which is nearly always better than the kiss.
There's also this: most couples remember surprisingly little of their own wedding day. It goes past at speed and in fragments. Photographs confirm what you already half-remember. A film shows you the parts you missed - the room reacting while you were looking the other way, the conversation in the corner, your mum during the ceremony.
Twenty years in, that's still the thing I get most out of this job. Handing someone a film of a day they only half remember and watching them see it properly for the first time.
If you can only afford one
Be honest about which kind of person you are.
Choose photography if you want something in the house, you're not likely to sit down and watch an hour of anything, and the idea of a film feels like something you'd file away. That's a completely reasonable answer and plenty of people give it.
Choose video if the sound of the day matters to you - a parent's speech, a particular song, someone's laugh. Especially if there's someone at your wedding whose voice you'd want to keep. That consideration outweighs almost everything else and I'd say so plainly if you asked me.
One thing worth knowing: couples who skip the film regret it more often than couples who skip the photographs. I'd say that even if I only did stills. The reason is simple - photographs are the format weddings default to, so you'll get some regardless. Guests take them. Nobody accidentally makes you a film.
If you're having both
Book them together if you can, and ideally from the same person.
Two suppliers who've never met will spend your day negotiating the same space. Both need the aisle. Both need the speeches. Both need you for couple shots. When it works it's invisible; when it doesn't, you feel it, and you're the one being asked to stand somewhere else.
One team means one point of contact, one look across your film and your photographs, and one fewer thing to organise. It's also cheaper than booking two separately - I price the combined collections below the sum of the parts, and most suppliers who offer both do the same.
What it doesn't mean
Having both should not mean two people directing you. That's the version couples are afraid of, and they're right to be.
The thing I care about most is staying out of the way. Nobody enjoys being directed at their own wedding. If the day would have happened more or less the same without me there, I've done my job properly - and that applies whether I'm holding a camera or a stills body.
If you find yourself performing, something has gone wrong, and it isn't your fault.
The short answer
If the budget stretches, have both - and get them from one place.
If it doesn't, ask yourself whether it's the look of the day you want to keep, or the sound of it. Your answer will be immediate, and it'll be right.
It's also worth reading what the films actually are before you decide, and what it all costs.