Modern browsers all attempt to adhere to common industry standards, but their specific implementations of these standards differ somewhat. The differences are fairly minimal, so if your site is also adhering to common standards, it's appearance on the various browsers will be largely similar.
If you find that your project is vastly more appealing on some browsers than on others, talk to your designers. They may be designing for edge features that are only present in select browsers, or for design behaviors that are known to work inconsistently across the differing browsers. Together, you can decide whether to "dumb down" the more edgy features in your design to even out the user experience across browsers, to tolerate the differences while implementing mitigation to soften apparent weaknesses in less appealing displays, or even to add tech that sends different designs to different browsers.