Photoshop is expensive, and has a very steep learning curve. It's also not focused on software design - which means that while it's powerful enough to do just about anything, it's not easy to use.
The problem with finding an alternative was that they were no good, either - they were either missing needed features, or their interfaces were too cumbersome.
Sketch 3 is the first great alternative that I've seen, and it's become our main design tool at work. There are a ton of things that make it wonderful; here are a few of mine.
Variable-height artboards. in Photoshop, I prefer using layer comps to hold multiple screen states in the same design file. Trouble is, some of those screens are taller than others (for example, maybe you have a long sign-up form, but a short forgot-password view). With Photoshop, you kinda have to choose one screen height. Sketch removes this limitation in a beautiful way with its artboards.
Easy grids. You can easily duplicate an object to make a grid - or if you're duplicating an artboard, it'll drop in at exactly the right place.
Sketch Mirror. You should always, always, always preview your designs on-device. There are tools for doing this with Photoshop (Skala Preview and XScope) but neither works reliably for me - I often have to reset them every few minutes. Sketch Mirror, though? Works every time.
Keyboard shortcuts. Zoom to a selection, zoom to canvas, rename selection, group, ungroup, toggle selection visibility, toggle selection lock - these keyboard shortcuts are your friend. Enjoy them.
Adjust the radius on a rounded rectangle. Yes, Photoshop technically has this, but it is far too finicky to be reliable. Sketch is great at this.
Easy asset exporting. I love using Slicy for exporting assets from Photoshop, but Sketch's built-in tools are vastly better.
Background Blur. This didn't exist in Sketch 2, which is partly why we continued to use Photoshop - with iOS 7’s blur effects, you need background blur to get your nav bars to look right, and while there is a clever workaround with Photoshop's Smart Objects, it's still relatively painful - Sketch makes it vastly easier to design with blur.
Presentation Mode. Press CMD+. to toggle Presentation Mode. No need to export comps to an InDesign file to then generate a PDF - just press the key and you have a great way to handsomely present, right from the design file.
The whole team can use it. Sketch is vastly more affordable, and it's a native app, so developers and testers feel more comfortable jumping in to the files, rather than having to wait for a designer to pull color, opacity, typography, layout, and z-axis stuff out of the costly-and-hard-to-learn Photoshop. It will save you time.
Sketch certainly has its problems, too - for one, the performance can get pretty slow with a complex design file - but it's improving faster than Photoshop is, and is so tuned towards software design that it's been a complete delight to work in full-time.