Under is not as aerodynamic as over because your arms are out to your sides giving a larger surface area for wind resistance. with certain types of under if the turn is sharp enough you may have to let go of the handlebar as it goes under the seat causing a potential issue with braking & control of the bike.
Over looks like you are begging for something, hence the term begging hamster. Also I have heard that over can give a false sense of security because you feel like you're "in" the bike & are protected more then with under.
2005 Performer Toscana, Kona Hoo-Ha, RANS V3 steel
USS (under) fans say it feels more relaxed and natural. It definitely offers a better view of the road. It also might be easier to mount/dismount the bike with USS. As mentioned, it is less aerodynamic (not really an issue for touring). I've heard that it is twitchier and harder to learn in the beginning. Also, harder to mount mirrors, computer, etc. on the bars. Could also be a small weight penalty. In a crash, you might fly off the seat (could be bad, or good if you land on your feet). Its harder to walk while pushing the bike along. Finally, recumbents with USS are less common, but there are some good bikes out there.
OSS is more intuitive. The bike will be faster because of the narrower profile. Its pretty widely available. By far most lowracers are OSS only. It offers a greater range of arm positions (hamster, superman). Its easy to find different replacement handlebars and stems. Easy to mount accesories. Its easier to push the bike, up a hill, let's say. One negative is that it may take longer to dial in if you have short arms, but its easy to make adjustments. Also, if your bike has a lot of tiller, it may feel slightly weird pushing your hands to the side.
OSS lets you mount your computer in front of your face instead of some compromise spot like on the shifter tube or on the frame, between your legs. The alien factor definitely goes to the USS - onlookers who aren't familiar with 'bent designs think you're steering by thought control!
I love the feel of USS -- it's like land luging! It did take some getting used to, however.
Getting in/out of a USS bike can be hard if the bottom bracket is high and you have anything mounted in the bars (like a hub shifter or a bell), because the mounted device presses into your thigh. USS also makes you more susceptible to a broken hand in a serious accident (see thread "Bike Accident resulting in 911"). As far as wind resistance, I've learned to pull my hands under the seat -- towards the middle of the steering bars -- to reduce my profile in higher speeds. Of course this is also a more dangerous way to ride than keeping your hands at the bar ends. I've exceeded 50mph without problems in stability or comfort.
One factor probably will have the greatest affect on your decision: the ease of attaching and accessing accessories, like bike computers, horns, and water bottles.