I think you have some incorrect information on your frames. The TCR Team frame you have a picture of looks like a composite frame, not an aluminum. Plus, Giant did not make an aluminum team frame in 2003. Starting in 2003 Giant made two TCR model frames. The TCR Composite and the TCR Alloy, which for Gaint means aluminum, not steel. The frames have identical geometry but are made of very different material. So, simply calling the frame a "TCR" without distinguishing between its alloy and composite version is incomplete starting with the 2003 models. Their Team frame designation for both 2003 and 2004 is a composite frame. Go to their website and you can see all of their models from 1999 through their current models.
Since you saw them both frames and know they are both aluminum, I think you are looking at a 2002 Team frame, not a 2003, and I don't think you have the correct picture of it. I think your designation of the TCR 2 as a 2004 bike is also inaccurate. According to the website, they made a TCR 1 and TCR 2 alloy bike in 2003, the difference being Ultrega v 105 groups, but only a "TCR" alloy bike in 2004, which has the Ultegra group. So, I think you are looking at a 2003 TCR 2 Alloy, not a 2004.
Consequently, I think you asked Giant the wrong question when you asked the difference between the frames since you asked them for the wrong years. You can see the difference, if any, by going to their website.
That said, it is little wonder you were unable to tell a difference between the two bikes. Both are aluminum and they have very similiar if not identical geometry. I do give you one word of caution. You mentioned an "upgrade" to the Ultegra triple group.[another reason why I think your are talking about a 2003 TCR 2 alloy since the 2004 TCR Alloy comes with Ultegra] You will note that Giant does not offer a triple as an option for any of their TCR frames. I, too, wanted a triple, was concerned that Giant didn't offer it as an option, wondered if it was possible to set it up as a triple, and asked dealers about swaping out for a triple. I received conflicting advice. One said no experience but didn't know why not; one said no problem; and one said he has tried it, the results were unsatisfactory, he wouldn't put out another one, and that Giant reccomends against it. He said the problem was that the chain stays were too short for the shifting to work properly. Given this conflicting advice, I wrote Giant and asked them. The following is the pertinent portion of their response:
"The honest answer is that you cannot install a triple chainring on the bike because the rear center distance is too short (400mm, needs to be a minimum of 407mm). If you did shifting performance would be constrained. For the future we will address this issue."
So, the answer is some people do it, you may be able to get away with it, but you may also be very unhappy with it. Giant made a suggestion I had already thought of which was to put a FSA Carbon Compact Pro crank on, a 50-34 double as opposed the standard 52-39. If you combine that with a 12-27 rear cassette you get almost the same gear range as the standard 52-40-30 tripple with a 12-25 cassette.
By the way, what else have you tried in a road bike?