Based on my understanding of Shimano's groups, you'll likely experience/feel some difference, especially in shifting, between the 105 and DA/Ultegra components. I don't know if I'd say it's $1600 worth of difference.
Assuming you're a recreational rideer, I tend to think that the Comp will meet your performance needs. I'm sure some will disagaree, but I tend to think that for the average recreational rider, the desire/need to buy a bike with higher end components is largely emotional. That's certainly what drove me to swap out some of the Mirage components on my Bianchi for Veloce. Even though I know Veloce isn't top of the line for Campy, I just knew I wouldn't be happy with something I perceived as an entry level bike (although I don't consider Shimano 105 as entry level; it's certainly a lot better than Sora or Tiagra). I'd also note, however, that I only spent about $200 to swap those things out. If it had cost $1600, I would have balked. With that in mind, I'd ask yourself how important it generally is for you to have top of the line stuff. If it's not that big of a deal to you, I'd go with the Comp.
Instead of buying the Pro, you could talk to your LBS--either when you buy the bike or later--about upgrading a few of the components. I'd start with the rear derailleur from a performance standpoint. That's not a terribly expensive upgrade. Also, your original post didn't indicate how the wheelsets for each bike compare. That's another place where it makes sense to upgrade. Of course, if my experience with buying handbuilt wheels is any guide, you can get a really good set of custom wheels for less than $500 that will probably perform and ride better than the wheels that come standard on either the Comp or Pro.
If it were me (and take this for what it's worth), I'd buy the Comp and spend my extra $1600 on some nice handbuilt wheels and some cute jerseys.
Kate