If I have two interfaces, one which gets its networks from EIGRP, and another that is an internet connection with VPN tunnels. If the same network exists for match address of the VPN tunnels and an EIGRP route, which gets priority?
Most specific route first. If there are multiple routes with the same mask, the one with the lowest "administrative distance" is chosen. I suspect the VPN tunnels end up being either "connected" or "static" (admin cost 0 or 1) and EIGRP is (IIRC) admin cost 90.
Based on this, I would expect the traffic to go across the VPN tunnel rather than out wherever the EIGRP routing is pointing. But I'd also test this in a lab environment before putting it in production and see what actually happens.