I leave both antennas on the rig and i doubt someone would want them.
People will steal anything they can grab, whether the item is of any real value or not.
I know this is an old post, but just to make a point I will relate a story about someone stealing a CB antenna I had on an SUV and some other thefts over time.
I had a magnetic mount CB antenna with a matched cable. As most 2 way radio savvy people know, you do need to have your cable and antenna and radio tuned to each other to a point to get the right SWR/etc. - so this one was right for my system. I had taken the handheld CB out of the truck but was lazy and didn't grab the antenna. Someone came along, dragged the magnetic mount across the roof of the truck scratching the paint and cutting the cable where it went into the SUV.
The antenna was of no use to them this way. They would have to have the equipment and take the time to tear apart a *sealed* antenna to properly attach a new cable. But they stole it anyway.
When I was in college some thieves came through the parking lot of the apartments I was living in and broke into a dozen or so vehicles. They stole the tools from my truck (broke a window to get into it) and stole the following from other vehicles; gloves, a pack of cigs, sunglasses, anything that wasn't nailed down essentially.
I had some stuff sitting in my carport some years ago - a rolling chair to work on vehicles, a jack to lift my motorcycles, some old computers I was going to throw away. One night someone came through and stole all of that stuff, including the old computers.
The point is that thieves will steal anything that they thing is even slightly valuable - even if it is just a pair of sunglasses. It may not seem all that big of a deal to you, but they will steal it if they can grab it quickly and run off with it. The more valuable it is the more time and effort and risk they will put into taking it.
So make it difficult enough that they will pass it by for something easier. Don't leave things out in view unless they are locked down.
Don't just throw a coat over something on your car seat because they will break a window to take the coat, whatever is under it and whatever is in your glove compartment - if the passenger compartment has a lot of stuff in it that doesn't look all that valuable, they will still break the window to rifle through your stuff.
I've seen this time and time again - last time was last summer some friends had a rig at a trailhead but parked the farthest away from the trail, there were multiple people around and some crackheads stopped and parked in front of my friends rig long enough to do a smash and grab even though people were around - they drove off before anybody could get a plate number. The damage they did was several times the cost of what they stole.
Thieves range from kids looking to have a thrill or trying to get some beer money, to drug addicts who will steal anything to supply their habit, to pros who can steal anything no matter how well it is locked down.