I travel for work often. I too have a 300 pound tough book that I have to lug with me. Our company has very strict policies about what types of activities are permissible on their computers. If you download non accepted programs on our network it will get you reprimanded, or worse.
When I'm on the road and not on the LAN, then I'm sure it is harder to track my activities, but to be safe I always carry a personal device. I own both the 13 MBA, and also run a mini. If I had to choose it would definitely be the air.
Stuck in a hotel room for days at a time, the air just provides much more opportunities for entertainment. I have 256 gb of storage that I can fill up with movies, and music. Also having flash, and utorrent provide me with infinite sources of content that are inaccessible from a iPad. Plus uhmmm you are stuck in a room with no wife so porn is much better on a laptop.
Plus using windows makes my skin crawl so the majority of work is actually done on the air. I have to write long reports, and respond to a million emails. Having the perfectly spaced keyboard, and great trackpad is a godsend.
If you bring your MBA along I'm sure you will find the company laptop collecting dust.
When I travel for pleasure I bring the mini. It served me well on a recent trip to Europe. I fly carry on only when going for personal trips so having a minimalist computer is great.
I am on the lookout for a good deal on a used 11 inch MBA for future trips, but even the 13 is all but unnoticed in my bag.