lay flat vs compact fold headphone case

i didn't do a TON of searching in this sub, so sorry if this question is common and i could have just read something else.

i have JBL Tune 510BT headphones. i use them a lot, and now that i am in college i am carrying them around a lot, and it makes me super anxious to have them just sitting loosely in my bag. i have traveled fine with them before and i don't care about scratches or anything, but i worry about them snapping or the swivel joints breaking. i was looking on amazon for a hardshell case and found several options, mostly being one of two styles: this kind of case where the headphones lay flat with the ear pads turned and facing the bottom, or this kind of case where the headphones are folded into their compact state inside the case.

they both have their pros and cons for convenience for me, one is more compact but the other is a lot thinner, so they come out to about the same for me, though i am leaning towards the folded case because it will take up less space in my bag. still, i don't know a whole lot about headphones and i do worry about the safety of my headphones when folded, because for whatever reason in my mind i feel like they would be more likely to break.

i don't care about brand or anything, i'm in the US if that matters, and my budget is probably around $20 max, i don't need anything fancy, i really just want to know if one style is generally safer than the other.

i kind of made this longer than it needed to be, but i just wanted to know what people would recommend, and if one style over the other is safer for them. thank you for reading my rant and for your help.