F-18C with a large number of AMRAAMs will be very slow and climb fairly poorly. Typhoon will massively outperform it in terms of getting an AMRAAM off first and will have an easier time defending in a BVR fight with both a height and energy advantage.
Radar quality will entirely depend on what radar it gets and what overhauls the Typhoon gets to its radar.
I think with a very light load, the F-18C might and I do need emphasise might be able to one circle a Typhoon and get a burst of canon fire off, but will likely loose any sustained fight without much effort from the Typhoon.
The Blue Vixen (ARI 50019) radar for the second-generation BAe Sea Harrier was regarded by many as being a better fighter radar than the contemporary AN/APG-73 used by later F/A-18 Hornets. Famously, when it was first used on operations in Bosnia, there were claims that it had picked up contacts that could not be detected by AWACS. - Source
Australia also nearly considered the Blue Vixen for its F-18Cs over the AN/APG-73 as it was equal and a lot cheaper but the intergration costs would have been too high