Basically, any type of remote access is only as secure as the security of your user's logon IDs and passwords. Although dial-up remote access may be more secure than broadband, it is still totally insecure if someone gets hold of your dial-up phone number and a user ID and password. Also, it is much too slow for most users and certainly for any type of connection between offices where users have to actually work over the connection rather than just downloading a few files to work on locally.
The optimal type of connection, speedwise, for this situation would be a terminal server. And even though this would be much speedier over a dial-up than a traditional RAS dial-up connection, it is still pretty slow, especially compared to the speed of today's computers that most people are accustomed to.
VPN was really designed for use over a broadband connection, because it uses PPTP and/or IPSEC tunnelling protocol for security. This means that the data that is transmitted over the VPN connection is protected. IPSEC is more secure than PPTP, but a lot of older OS's don't play well or at all with IPSEC.
What I would say would be the best possible solution would be a terminal server over a broadband VPN connection - best combination of speed and a reasonable level of security.
Hope this helps!