I very much enjoy that it syncs with my mobile and desktop, so that if I need to run to a meeting I can still receive notifications (and use the app) from my phone.
Having my Hangouts conversations indexed with my gmail makes me life much easier when I can't remember if I had a conversation with someone via email or chat, and I can just search in one place to find what I need.
I do struggle sometimes with syncing issues, where mobile or desktop will be behind the others. I haven't quite figured out why it happens, because sometimes I have both devices sitting in front of me and I haven't moved/switched from wireless to data/etc.
Sometimes my sound notifications just randomly cease to work for periods of time. Same thing, nothing has been moved or changed, but I suddenly no longer receive sound with my notifications (which as a busy person, I sometimes require to get my attention).
I also like that I can view if someone is viewing from their mobile or desktop (if they have that setting turned on, of course) - it helps me monitor my staff and understand how they work. I've found that some people are just much more responsive from their phone because it's always on them, whereas others don't check it at all and have to be at their computers to be productive and responsive.