Batboard

I am wanting to put some scanner antennas on my car using NMO trunk mounts. I'm wondering what would be better for RX on rpeeaters about 20-40 miles away. What would be better on UHF and 800 (2 antennas), 1/4wave whips or the Antenex Phantoms? They would be on the trunk, on the edge near the window, or possibly on the sides about 8" from the window.

If you're trying to hear repeaters that are 20 to 40 miles away you'll
be better off with gain antennas. The 800 mHz Antenex will probably offer you a 3db gain but I'm thinking that their 450 mHz unit is probably unity. I run a 900 mHz Antenex Phantom on my car from a GTX M11
radio running 13 watts and the performance is okay but not much more, and they claim 3db for the antenna. Overall, if you have the space, running whips with 5db or more gain would probably work best.

For a VHF/UHF/800 Scanner antenna I use a 800 5bd antenna. It is the one Motorola shipped with the Astro Spectra. It has good recieve on all bands but low band. You may try one of them. Good luck.
Radio Kid

For receive only, I've always had really good luck with a 1/2-wave VHF. It does really well on most bands, at least 30-40 miles on UHF and better on VHF. (IIRC, the 1/2-wave VHF is unloaded, needs no ground plane, and just appears as a random length wire in the other bands, right?)

If you're really after weak 800 MHz, I'd lean toward a 5db 800 MHz antenna. Maxrad has a double-coil triple-collinear thing that's about 24" long and does pretty well on UHF and VHF too, although it looks a little like that Radio Shack mag-mount scanner antenna. You could put either on the trunk lip.

My limited experience has been that for receive-only, a larger area to catch the signal makes more of a difference than resonance at a particular frequency.