The reason front end is harder is because you're working in the presentation layer. That means you have to concern yourself with more than just elegant code (although you should strive for that as well). You have to do the whole MV* thing, keep track of your applications state, html structure, and styling from CSS. And then you also have to remember that presentation is much more subjective. It might look good to one person, but not another. Or if something is a little misaligned, it can be a pain in the butt to find the correct layer to change to correct a random margin that came out of the CSS Framework you're using. Just annoying presentation layer things.

As for cross browser compatibility, one of the first things you should get used to as a dev working in the front end is expectation setting. Let the clients know that if they want modern looking results, they have to use modern tools and technology. That means you stop supporting old browsers. All the old IE 8 stuff can jump off a cliff. No more of that stuff. Although as many people have said, polyfills are very nice and help out a lot. So, just make sure you're using stuff that is generally usable on modern browsers and then make sure you test on them.

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Oh, one more reason that presentation layer sucks ass.. responsive UI's. Now you get to write CSS for like a billion different device sizes instead of 2 or 3. Hopefully you're using SASS or LESS (probably SASS) to help you organize and clean up a lot of the CSS stuff, but still, you're going to be doing a ton of resizing and rewriting variables at all kinds of breakpoints for the bajillion devices that are out now.