I have very similar tastes to my closest friend and to one of my cousins, and we often seem to independently buy the same or very similar things at the exact same time. Clothes, bags, things in our houses, even to the point that two of us have children who share a name (there are reasons but they are outing to get into).
We've usually laughed it off and been pleased about the coincidence.
The only time I've really minded someone buying the same things as me is when MIL used to do it. You would buy something, she would make a snide comment about it, then go out and get the same thing, then still be unhappy as she'd wasted money on something she didn't really want, thinking it would make her happy but it never did. She was a woman who was never happy with herself or other people, she's not good in her own company, can't be alone, and I don't think she had much self awareness to just be herself. So she would copy others whilst also putting them down for liking what they liked, and then still be disappointed because doing it hadn't brought her any joy.
I had to google the bag from the guess on the thread here, didn't even realise that lv was Louis Vuitton at first. I'm with you, it seems like a popular design, I know I've seen a lot of similar bags before, and if you like it and it will suit what you need it for, I can't see why your friend is so upset.
It sounds like you've chosen a bag that will best suit your needs and she's chosen a bag she thinks will impress people due to the cost.
I still can't see why you can't both have one if you both love the bag. I think the deciding issue for me would be if this is an unusual request from her and how she normally behaves about having things others don't. Perhaps also if she has lots of expensive things to show off, or if this is a one-off. Is she usually pleased for other people when they have nice things, or is she jealous?
I have a bag made from old firehoses, I have not had it long so I can't speak for how durable it will be, but it's survived being dragged about as firehose for many years before being turned into a bag so I'm guessing it will be good. It's a fraction of the cost of your bag, looks great, has a bit of individuality about it, and is big enough to fit everything I want and need to carry (and more). I definitely recommend it so far. I opted for one that still has printing on it as I felt it added a bit of character, and I love it. It's from a company called Elvis and Kresse and they donate 50% of their profit back into charities for firefighters. They have a great range so well worth a look.