Frankly, both.
Boeing's point-to-point strategy is all very well, but there are airports such as LHR, FRA, etc where it is not possible to fly any more planes. The airports are full. This is where the A380 will rule.
Conversely, there are airports that see little traffic and have plenty of room for more, smaller traffic. Boeing's strategy says that the passengers want to fly directly from there to where they want to go, so that needs smaller, longer-ranged, more efficient planes which is what the 787 is.
The media and many nutcases on airliners.net forums believe that one or other approach will win.
Both are entirely valid. For example, 787 or no 787, no airline is ever going to fly point to point between leeds-bradford int. and ontario CA. Or Prestwick to San Diego. Thus you have to go to a busy hub airport, and fly to another busy hub airport to get on a plane to where you do want to go. So... the A380 allows expansion of capacity at slot-limited airports like LHR.
Another point is that departures are timed such that you arrive at a reasonable time of day. That's why QANTAS and BA have flights from LHR to melbourne within a few minutes of each other, despite code-sharing and the oneworld alliance. If you want more capacity to MEL from LHR do you put a third flight on? Are there enough passengers for 3 full 747s, or is the third aircraft going to run at a loss most of the time? And this is where the A380 makes sense also.
But the 787 makes a lot of sense too. It's a longer-ranged, more efficient replacement for the 767 and 757-300. It will open up profitability on a route like Manchester - San Francisco which is too low demand for a 747, A380 or 777. So, you no longer have to change planes in chicago or atlanta, get there quicker, etc.
Commercially, both projects are doing very well. The A380 needs more sales to break even, but this is a long term project. It's not about sales in the first year or two (and let's remember, it hasn't flown yet). It's sales over 15-20 years. The 787 has plenty of sales, but it doesn't yet physically exist and is bringing so many new technologies to the industry that it's more of an unknown. It's also a much cheaper plane than the A380.
Overall though, Airbus outsold Boeing for the first time ever in 2003. The feat was repeated in 2004 with B's market share down to 43%. Competition is good though, as it drives the industry forward.