Its really not a matter of either-or or 'instead of'. In grossly over-simplified terms, VRF is to Layer 3 (kind-of) what VLANs are to Layer 2. VRF is there to logically divide L3 topologies - to provide a means to create multiple, autonomous routing topologies. A given VRF instance in a given environment could technically consist of many different VLANs - each with their own associated SVIs - all a part of that VRFs L3 routing domain.
For example - you could build a data center where you host multiple customer environments. Each of those customers could be on their own VRF (actually in this design it would probably be VRF-lite) instance. Each of those customers VRF's could consist of dozens of VLANs that each use an SVI as its gateway for inter-VLAN routing - all converging back to the core router where the VFR is defined. The core router is where (for example) Internet or B-to-B (including inter-VRF in the case of VRF-lite) routing is provided.
In reality, VRF is much more complex than this and would require MUCH more writing on my part just to impart my limited scope on its nuance ;-) But I did want to iterate that VRFs and VLANs are *not* mutually exclusive at all.
