I tried switching from QS to Alfred ages ago, since Quicksilver development has been stagnant for over 5 years (it's still being updated, but just barely — mostly just compatibility-related improvements).
So obviously you can deduce from my last sentence that the biggest advantage Alfred offers is that it's actually under active development. New features are added pretty regularly. Just last month they added some new stuff. Nothing game-changing IMO, but it's a massive difference from Quicksilver. (New features occasionally appear in the QS change log, but they're almost universally trivial — for example, in the latest release they made it prompt you for what to do when there's a file-rename conflict. That's the level of 'feature addition' you can expect from QS.)
As a result of this active development, Alfred has a vibrant community. Their developers are easy to reach via social media and e-mail, they have a forum, a blog, tech support people, &c. They have lots of users who like to share their work-flows and settings. Quicksilver's community was once like that, but it hasn't been for many years. I don't think most people even realise it's still around. The Web-site design/structure hasn't been updated since ~2010, giving the impression that the project is abandoned. Much of its extended functionality is buried in esoteric third-party plug-ins, and documentation is often out-of-date or simply non-existent.
Alfred is much prettier by default, its configuration interface is so much more elegant and intuitive, and it's a lot more dynamic in the sense that the UI can be moulded to better suit certain features (for example, the music-player feature adds media control buttons to the interface). The Quicksilver interface is pretty much static no matter what you're doing, and it's honestly not suited for a lot of the functionality people have tried to inject into it (like clipboard management).
Alfred is also vastly more stable and reliable. Hard lock-ups and silent crashes are an almost weekly occurrence for me on Quicksilver, and the auto-updater seems to break periodically, so that every 3 to 6 months i have to go manually download the latest version from the Web site.
With all of that said, i'm still using Quicksilver, and the #1 reason for that is the fact that it handles its own catalogue index. Quicksilver has very powerful custom file-indexing options, so that for example you can control exactly what types of files it catalogues under what directories, how many levels deep it goes, &c. Alfred, meanwhile, uses Spotlight, and only provides global (as opposed to per-directory) toggles for a few basic file types like 'folders' and 'images'. As a result, finding things in git repository directories and similar complex file structures can be very tedious.
The other main advantage QS has over Alfred is that it's free and open-source, which is important to some people... but it's not to me. If it weren't for my very particular file-indexing needs, i would definitely switch to Alfred.