No, they use the same fundamental hardware and both OS's are more than capable of doing the work we do in Design. The only real difference (to the user, not the techy who cares about the unix core to os-x) is the way the interfaces are designed. Obviously this is comparing with like for like specs etc.
If your laptop graphics is not crisp then you need to check your output settings or if it's purely a visual thing based on the screen you may need to compare the physical hardware and what the resolutions are etc.
I've been pro-Mac for a long time but lately I feel they've been pricing themselves out of the market without bringing the right features or specs to stay competitive. Potentially fewer worries about security may be a consideration but that's not the advantage it used to be and you should protect and maintain your system no matter the platform.
In terms of the graphics being sharper, no matter the configuration Macs that come with a display always come with a fantastic one. I don't know what display you're using with your Dell or what resolution it is but lower-priced PCs nearly always sacrifice screen resolution first. My wife's £500-ish laptop is about a year old and it's not even 1080p. Check the resolution on both devices.