The main benefit of having an SDN controller administer TE tunnels is the centralized view of the entire network that it provides. Having multiple controllers with a distributed database, with a centralized view of the entire network, may be a valid deployment model in large networks that dictate distribution to enhance scaling.
SPRING and BGP-LS are orthogonal (note that other - non "-LS" extensions to BGP exist to carry SPRING labels). BGP-LS is used by an SDN controller to collect the TE database from the network, whereas RSVP or SPRING might be used by the router to establish TE tunnels in the network, as instructed by the SDN controller through the Path Computation Element Protocol (PCEP). The current implementation of Juniper Networks SDN WAN controller (that is, NorthStar) supports the combination of BGP-LS (to collect the TE database) and PCEP with RSVP extensions (to administer TE tunnels), whereas the new release coming out this year (2016) will support combinations of BGP-LS, PCEP with RSVP extensions, and PCEP with SPRING extensions. That is, the SDN controller will be able to instruct (through the PCEP) the router to establish TE tunnels by using the SPRING paradigm.