I've got and used both shelters in a selection of Scottish weather (often with Colin actually), and very simplistically I'd suggest that the DuoMid handles wind well, and the steeper sides will tolerate snow loads better than the Trailstar. The Trailstar can be pitched very very low to the ground very quickly and thus sheds wind particularly well. The shallower sides will of course not tolerate snow loads as well as a steeper-sided pyramid shelter.
The beauty of the Trailstar, as Hendrik suggests, is the pitching time, in foul weather you can stretch the Trailstar over your gear and peg out, before getting under cover and erecting the centre pole (a collapsable pole helps here). Further adjustments can be made from inside if necessary. It's also cavernous, even when tight to the ground. Colin likes to take his inflated packraft into the shelter next to him (but the other side of the pole), but this probably isn't the place to discuss Colin's inflatable tendancies.
The weakness is the entrance door - if you keep one side raised to form a doorway (by no means essential) you don't want this facing into the wind, but again it's no big hassle to either collapse the doorway or relocate to an alternative side. It's symmetrical after all. On one windy night I collapsed the centre pole to the extent that I had to slither in on my stomach (all in the interests of experimentation of course, it was a touch unnecessary) and it was incredible how the wind flowed over the shelter.
I find that the DuoMid takes a touch longer to pitch as it's quite important to peg out the first 4 points as square as possible to get a taut pitch, plus the extra complication of a zip. That's not to say it's a long process, just a bit longer than the Trailstar!
There's a little bit about both shelters on my blog at: http://phil-turner.net including a recent trip to Finland where both a DuoMid and a Trailstar were used on an initially breezy evening (DuoMid pitched 'end-on' to the wind, Trailstar with opening on opposite end). I've also posted a YouTube video showing how a 'less-than-taut' DuoMid pitch can be a bit mobile in a decent breeze in Scotland. You'll have to do a search for that, can't access the link right now.