re:
Or do you think alterations are worth it to have this dress to wear in general?
Well, I guess it depends on how much you like this dress. I like it a lot, and I think it likely quite a bit nicer than the other one, based on the fact that it's silk. But you are the judge of whether it's nice quality or not.
I also like the pleating/gathers and the not-quite-black colour.
You could wear it with oxfords or fancy shoes - in other words, you could wear it in more scenarios/settings than the other dress. So generally I think it is a more versatile dress.
If, on the other hand, you get fancy shoes and wear your sister's dress, then you have a dress that you only like a little bit, and shoes that you can only wear with that dress (unless you have other stuff to wear fancy shoes with). In other words, a less versatile combo.
I would *also* try to find a fancier shoe to go with the silk dress, but that's because I like fancy shoes. I think you can pull off oxfords+dress.
I don't understand the comments about the sleeves being the wrong length as they look fine to me, but my eyes are untrained compared to others'.
Like your haircut by the way!