Ask which headphone someone should buy and the useful first question back is not about budget. It is: what is the room like, and who else is in it. The enclosure, open or closed, settles more about how a headphone works for you than almost anything else on the specification sheet.
What the enclosure actually does
A driver moving in a sealed cup has to compress the small volume of air trapped behind it. That air acts like a spring, which stiffens the driver’s movement and generally lifts the low end. An open back removes the spring: the rear of the driver vents to the room, so it moves more freely, and the low end depends more on the seal at your ear than on the cup.
The audible result, broadly, is that open backs sound less enclosed. Sounds seem to come from around you rather than from a line between your ears. Closed backs sound more contained, and in poorer designs the trapped air produces a boominess that does not go away.
The trade you are making
Open backs leak. Anyone within a couple of metres hears what you are hearing, and you hear the room. In a shared office that makes you the person with the leaky headphones; on a train it means you turn the volume up to compete with the carriage, which is bad for your hearing and bad for the music.
Closed backs keep sound in and some of the room out. How much they keep out is a measured quantity that needs a proper test report, so treat any isolation figure quoted without one as marketing. Passive isolation from a well-fitting closed back is real, but it is far less than a sealed in-ear with the right tips.
The room is part of the system
An open back in a hard-surfaced room with a fan running is not doing what it was designed to do. If your listening space has a floor you can hear footsteps through, a closed back or a sealed in-ear is a more honest recommendation than a wider soundstage you will never hear under the noise floor.
The same logic applies to speakers. A nearfield monitor is designed to be heard from about a metre away precisely so that you hear more of the speaker and less of the room. Move it further away and the room takes over. That is why a monitor on a desk and the same monitor across a living room are two different products.
A reasonable answer
If you have a room you can close and nobody minds, an open back is likely to be the more enjoyable listen for the money. If you listen in shared space, on public transport or next to someone working, buy the closed back or the earbuds and do not feel you have compromised. You have bought the one that suits where you actually are.
Plenty of people end up owning both, and use them for completely different things. That is not indecision. That is two tools.