I don't know what component group the 2010 Trek had. I would guess that it was either Apex, or 105. Tiagra was still 9 speeds in 2010, so 105 was the minimum Shimano level for 10 speeds. The way that Trek has usually done their component levels, 1.1 = 2300, 1.2 = Sora, 1.5 = Tiagra, and 2.1 either Apex or 105. More likely Apex.
Biggest differences? Trek's 200 series frames are better than Spesh's A1 frames.The 2300 group on the Allez is basic entry level components, 8 speed, and you can't shift comfortably from the drops. The entry level Allez has **** wheels, and flat-o-matic tires. However, being used, you have to check out the Trek carefully, for possible crash damage. Apex components, if that's what is has, aren't horribly expensive to replace. If it's the original chain, you may have to replace both it and the cassette. A PG-1050 cassette doesn't cost an arm and a leg, though. I'd feel better if you were buying it used from a reputable LBS than privately, but if you take someone who knows bikes with you, that minimizes the risk. And by all means, insist on riding it first.
Couple of last points. If the Trek isn't the right frame size for you, it's a bad buy at any price. A Specialized dealer can size you to a new Allez. Also, SRAM shifters, if it has an Apex group, work a little differently than Shimano, but it's not a very steep learning curve.