Both of this tools use the same encoders under the hood, what you see here is just comparing different settings in default presets they provide. If you would like to experiment yourself with x264 encoding you can find descriptions of possible options here http://www.chaneru.com/Roku/HLS/X264_Settings.htm
I've used ffmpeg/x264 professionally and personally and I'd not suggest this for the average user. It's a bitch to get all the settings right.
If you're building an automated system to transcode video ffmpeg/x264 is great (or better yet, use an online transcoding service). For an average user go with Handbrake.
