The problem you see is not the browser's fault: it is the designer's fault. There are two basic length measurements used in web pages - relative and absolute. If these are used inappropriately the page will only fit together on a browser using exactly the same font size and page scaling as the developer did.
You, as the user, set the page scale and font size, although obviously each browser will also come with default values.
Many (I'm tempted to say most) web designers are incompetent. They produce pages which look pretty on their client's browser at their client's screen resolution, treating the job as a page layout job rather than an information-conveying one. They get the contract because most clients are advertising agencies or big corporations who expect to control every aspect of appearance, so they are pleased by what these cowboy designers produce. Real designers who stick to HTML and CSS principles don't get the contract because they produce pages which always make sense, but don't always look the same, which isn't what the corporate bosses want. There is a philosophical contradiction at the heart of the web - it relies on rules written by anarchists! I mean the rules are written to put the viewer in control, because of a deep freedom-loving philosophy. Big corporate bosses think the producer, rather than the viewer, should be in control, so they can't cope with that philosophy at all.