I much prefer Alinea, but they're vastly different. Tru specializes in more contemporary French food. The style is somewhat traditional French, although they bring in very modern ingredients. The dining room itself is more contemporary.
Alinea is very modern in food and approach. You'll often find very nontraditional elements in a dish (e.g., vapors, powders, pillows, etc.) While Alinea has some detractors, I think it's an amazing dining experience that can be duplicated at only a few restaurants in the world. Here's a link to both the restaurant's menu and a very recent review with some amazing photographs:
Personally, I'd take Alinea any day of the week, but if you prefer more traditional dishes, you might prefer Tru.