Generally, they are interchangeable, but planning to systematically upgrade parts is a terrible idea. Bicycle manufacturers purchase parts at such dramatically lower costs than even your bike shop can that this plan is economically idiotic. You will save considerable amounts of money just buying the level of groupset you intend to run.
Take note that front derailleurs are pretty sensitive to good setup--a lot of what you felt between the two groups could have been the quality of the mechanic who set up the bike. Also, better quality cable housing may be on the Ultegra bike. The shifters (which are insanely expensive to upgrade!) might account for a very small difference in shift feel. The FD probably makes very little difference. If they're both actually Shimano cranks/chainrings, I'd be very surprised if there were any shift performance there, either.
Well setup 5800 shifts very well in general. Aside from weight, the main thing I perceive between the two is the feel of the shifters. The rear derailleur pullys are also better on Ultegra. The tolerances and surface treatments on Ultegra are a little better.