Congratulations on your life altering decision. If you manage to do it every day, you will melt away the pounds. I've dropped about 15 in a few months, and I didn't think I had any to drop!
I think both of those bikes are pretty similar and will get you there. One of the things I would key in on is wheel quality. At 270, you will put some stress on lesser wheels. The Trek comes with WTB Dual Duty rims, which from WTB's web site looks like a strong wheel. I don't know much about Alex rims. Also, make sure you keep your tires pumped up to the maximum p.s.i.; if you don't, you'll have to work really hard and you'll be getting some flats.
When you start riding and run in to the inevitable problem, don't despair. Ask questions in this forum as you already have. It's a great resource.
Did I say to keep your tires pumped up?