In your situation, I'd stick with OSPF since you have a dynamic-routing-capable device sitting behind the two edge routers.
VRRP is a "first hop redundancy" protocol, and does not address whether the active router is actually capable of forwarding packets further.
Suppose router1 is the active router, but that router1's internet connection is down. VRRP will still advertise itself as the active router.
OSPF, if it originates default GW information "if-installed" is much more effective since you're using BGP.
If the Internet goes down on router 1, then router 1 will stop saying "I'm the default GW" in OSPF, and the other devices in the OSPF cloud will learn this, and route to some other gateway.
If the ISP has correctly configured their BGP, then suppose the link to ISP1 is up, but the ISP1 router is isolated from the Internet - it should withdraw its default GW from you, causing your OSPF to stop announcing R1 as the default GW.
VRRP just says "I'm alive"
When given a spoon,
you should not cling to your fork.
The soup will get cold.