Based on my second (or third) hand knowledge, there are some advantages of Ultegra over Tiagra, but none of them would lead to being able to push a bigger gear.
The advantages according to those that use high end groups like Ultegra are (not necessarily in order of importance):
1) Crisper shifting
2) Slightly lower weight
3) Looks better
If you are finding that you're able to push a bigger gear on your TT bike, it is likely to be because of your riding position, or possibly tires. Even wheels (the #1 thing to upgrade) are typically seen as beneficial for acceleration and climbing, not pushing bigger gears once you're moving.
Tires on the TT bike could have lower rolling resistance, and this could help you push a higher gear, but the number one force you need to overcome when riding on a flat road is wind resistance. Your TT bike would probably be less comfortable for a long ride than your road bike for the same reason that it is faster... You are in a more addressive riding position.
For climbing (in case that is what you are referring to) there is an advantage to losing every ounce of weight that you can... since you are in effect lifting extra weight for every inch you climb... Whether Ultegra gives enough weight loss to be noticed would have to be up to you... But if climbing is your issue, I would say that the bulk of the difference would be bike weight, and you could possibly do better for the dollar by replacing wheels than upgrading to Ultegra.