Synology NAS offer both AFP and SMB2, Mavericks always choose AFP
When you access a file share, you could try using CMD + k in Finder (Connect to server), and then type the address as a CIFS or SMB path - ie.
cifs://my.server/SomeFileShare or smb://my.server/SomeFileShare
Disclaimer: I don't have Mavericks, and no access to my Mac right now. And I'm not even certain that Finder doesn't somehow jump on AFP anyhow.
Edit:
Ok, I can understand that you don't like to do the clicky-clicky every time.
Here's a description of how to set your OSX account preferences to do the SMB mount for you at login: http://www.howtogeek.com/howto/21600/mount-a-windows-share-in-os-x-and-have-it-reconnect-at-login/
-and here's a slightly more technical recipe for making OSX automatically mount the SMB shares when needed by editing the fstab: https://superuser.com/questions/336665/how-to-automount-smb-shared-network-drives-in-mac-os-x-lion
Regarding priority, Apple says (http://support.apple.com/kb/HT5884) that in Mavericks SMB is the default protocol, and if not available, it will fall back to using AFP. This seems contrary to your experience, which makes me think that maybe you upgraded from Mountain Lion, and somehow the (hidden) setting of file protocol prioroty didn't get changed according to spec.
The link also says how to force a specific protocol:

To connect to a file server directly, use the Connect To Server feature of the Finder. Select Go &gt; Connect To, and enter a URL, IP address or DNS name.
You can attempt to force a specific connection protocol (such as SMB or AFP) by using a valid URL. As long as the server you are connecting to allows the protocol you specify, the URL should work.
smb://ServerName/ShareName
afp://DOMAIN;User@ServerName/ShareName

Same disclaimer as above - I am only on 10.8, so everything might have changed in Mavericks.