What they have in common is that I still listen to / watch them probably about once a week. They are both brilliant.
If I could keep only one for the rest of my life I'd go for Encore. It has a great happy, relaxed, content vibe to it. The arrangements are superb, and Neil's voice has a wonderful range. Just as a collection of CH songs it would do, because the Encore versions of those songs are among the best I've heard. And I love Neil's happy grin at the beginning: It's an amazing occasion.
FTTW has a lot of nervous energy, which leads to some great noise (several of the songs are faster, louder, rockier than in Encore). I love the versions of Locked Out, There Goes God, Private Universe. And Sister Madly and Italian Plastic will make anyone smile. Because Paul.
Sometimes the sadness of the occasion (and Paul) catches up with me, though. I haven't listened to the FTTW version of DDIO for years, just like I hate watching the last episode of some beloved TV show.
I'm just glad we have them both. (And others as mentioned above.) When I need to let off some steam, turn the sound up and go a bit mad and/or silly (typical weekday evening) > FTTW. When I need amazing music that reminds of how lucky I am (typical weekend) > Encore.