MPLS or IPsec VPN:

Virtual Private Network (VPN) is a connection method used to add security and privacy to private and public networks. Because of strong encryption, data traveling over VPN is not visible. In lay terms, the connection is thought of as a pipe in a pipe -the outer pipe being the internet connection. Secure VPNs use cryptographic tunneling protocols such as IPSec to provide necessary and intended confidentiality. VPN can be created using various encryption technologies such as IPSec, SSL and TSL.

On another hand, MPLS is a mechanism that directs and carries data from one network node to next. Highly scalable, protocol-independent MPLS assigns labels and decisions are made regarding where they will be forwarded. MPLS operates at layer 2.5 - which lies between Layer-2 ( Data link layer ) and Layer-3 ( Network Layer ). It can carry varies traffic ( IP Packets, ATM and Ethernet frames, etc.). Unlike VPN, MPLS is a protocol independent mechanism.

According to fs.com :