Niether of the bikes you mention are built for 300lb. riders. Don't be fooled by the fact that the guy selling you a Trek will tell you there isn't any rider weight limit. That just means Trek won't refuse to warranty a part based on your weight--not that the bike will actually handle your weight.
Trust me, I 'm a mechanic at a shop that sells Treks. I don't mean those bikes are certain to break on you, but that they might.
For a 300lb guy the weakest link on any off the rack bike is always going to be the wheels. You can help out your wheels by using larger tires, which will protect the rim a little bit. I don't see why you'd go under 35mm's. Some dillweed is sure to spout some crap about rolling resistance if you go with the larger tires. They're wrong, it won't matter much, but it is a subject for another thread.
Forget a modern road bike, they will not be practical for you because they're essentially racing bikes. The handlebars will be too low for your comfort becaue the pre-cut steerer tube will be too short. A 300lb person puts a lot more pressure on their hands and wrists than the average bear. The frame on modern road/racing bike will also severly limit your tire choice. You'll be lucky to fit 28mm tires, forget anyting bigger. This isn't very practical for commuting for a rider of any size, much less your size. And forget mounting fenders on most road bikes should you ever decide to be more than a fair weather cyclist.
Your best bet is cyclocross bike. If you came into my shop I'd recommend a Surly Crosscheck. Plenty of clearance for large tires and fenders if you wish. Also, since you can buy the Crosscheck as a frame only, we can make sure to pick out the right parts for a guy your size. The steerer tube on the fork won't be pre cut too short, so we can get the handlebars the proper height without using steerer tube extensions or a high riser stem. We can pick exactly the right wheels for you. I wouldn't even think of putting you on anyting under 36 spoke, and it wouldn't hurt to use Shimano 40H tandem hubs. A heavy-duty or tandem rim will work. Velocity Deep-V's or Dyads will work. The frame of a cyclocross bike is going to be more reliable and robust since it is made to go off-road.
You're going to need good advice, and if you have friends into cycling you are likely to get a lot of bad advice. You'll probably get some more from some bike shop employee. A 300lb rider is a special case, you have to have the right equipment. Understand that mass produced bikes are spec'd for average people. Very short, tall, or heavy riders have to go outside of the box a little bit.
Again, that doesn't mean another bike is going to explode on you. It might work fine for awhile. But it won't over the long run. Two weeks ago I had to help out a 300lb guy after some jackalope of salesman sold him a Trek 1500. The wheels were toast and had to be retrued after every ride. You might spend a little more getting the right bike at first, but if you plan on riding regularly, it will be more than worth it in the long run.
Also, don't let anyone put you on a bike that is too small. No more than 1.5 inches of standover clearance. Anything else will make it hard to get your handlebars to the appropriate (for you, at least saddle-level) height.