Sketch's main benefit is that it's built from the ground up to focus on vector-based design and composition, with a more modern, simplified approach to its interface. It makes it feel really light-on-its-feet and productive for UI design.
Photoshop is a powerhouse but has a lot of historical bloat built up over the years particularly around high-resolution bitmap editing. I mean it can paint a car out of a scene with a single brushstroke for chrissakes. Sketch has none of that, but in turn its vector feature set is super streamlined and thoughtful, so it's basically a UI designer's dream.
It would make a little more sense to compare it to Fireworks (may it rest in peace), as that was maybe a bit more suited to UI design than Photoshop.
My biggest benefit is working with multiple artboards. As we all know, design now starts with going mobile first. Right from the start there is a mobile view, tablet view, and desktop view.
Other pros
+ Text Styles (Save a font style for h1,h2,h3,p. Why hasn't anybody else done this?)
+ Better color picker because it magnifies to the pixel. Much easier/faster to find colors on text.
+ There's like 10 colors on your active palette. Photoshop is 2.
+ Faster to export images.
+ Duplicate/Copy anything faster than Photoshop.
+ Opens up way faster than Photoshop. Similar to opening a text editor.
I'd say there is zero learning curve. So much easier to get started for anyone new. My favorite thing about Sketch is the ability to use Pages and Artboards + Symbols for multiple screens design. That's the way I prototype nowadays; focusing on interactions and flows rather than static single screens and branding/image editing.
I think the most fundamental advantage is that Photoshop was designed to edit photos, whereas Sketch is clearly built for UI design. Because of that, it has the tools you are more likely to use in the right places and has a lot of built-in features specifically geared to designing UIs.
