I guess it depends on how large your library is.
What I do I have my Calibre library (10GB) on my Dropbox account.
The benefits are:
- Access no matter where I am, or what my network is
- Fast access on any machine, since they're all local
- Dropbox acts as a library backup
- All computers with the library stay in sync, even if they aren't physically located on the same network
- I can have it on my work machine for access to my work-related books in my library.
- Low maintenance, no need to manage file shares.
- Access on my phone via MoonReader app, which has built-in Dropbox support.
Downsides of course:
- Duplicate libraries on every machine, so more space usage
- If you have a large library, you'd need the the paid Pro account (which I have)
Dropbox works for me, I just set and forget.
Downside of NAS would be configuring for secure access outside your network.
Upside is it's cheaper though. :-)
I've been using Calibre with Dropbox for years, since before Calibre was 1.0, with no issues.