I'm not a fan of the current system for a number of reasons.
There is nothing that says that agenda score is the defining measure of success - decking the corp or killing the runner are both legitimate game wins in their own right, but they are not represented when computing score for a game loss. Hence the format disfavours playing them as anything but a secondary strategy because when they fail or misfire you end up with nothing.
The winner of the first game can play to time out in game two to guarantee a win, especially if it looks like he will lose by a larger margin than he won the first game. This turns a 4-2 loss into a 5-1 win. Stalling for time should never be a valid strategy.
Both games carry the same score weighting - i.e. they contribute equal value to the overall score. But they don't necessarily receive an equal share of the time. Very few people will rush game one to try and secure a fair crack at game two, but very often game one will over-run and players will be pressured into mistakes in game two in order to try and play a full game.
The tournament format causes you to make play decisions that you wouldn't make if the game occurred in a vacuum. For instance: do you rez an archer, knowing that it won't keep the runner out of the server for the winning agenda? In a one off game you rez it every time on the off-chance that it makes a difference (particularly if you can trash programs like Net Shield or Deus X that might make the runner think the card he's about to hit is a lethal trap), but in a tournament game is it worth holding onto the agenda point(s) and conceding the loss? Similarly, I had a game go to time recently and my opponent on his final turn scored a Hostile Takeover out of hand to improve his score, but that was absolutely the wrong play if the game was continuing and he had been trying to play for a legitimate game win. @Alexfrog also mentions the "target" agenda score from game one that will secure the match.
The format also means you're locked into a matchup for a full 60+ minutes against the same player. I think this is fine at the highest level but for social play I would prefer to play against a more varied crop of people.
My suggestion would be to reserve the two-match setup for KO brackets in big events and just play single games for the swiss stages. You could probably devise a neat method to work out pairings, but a basic approach would be:
A] Split the field in half
B] One half plays corp for 3 games, the other plays runner.
C] Then you switch and play 3 games in the opposite role.
By this point the two halves of the room will have played 6 rounds of swiss, but not competed against anyone in their own half of the draw. So now:
D] Each half plays its own 3 round swiss
By the end of the swiss everyone will have played 9 games against a cross section of players.
For the last 3 games you can either determine who plays corp/runner randomly or let the lower ranked player choose (if you assign fixed roles or let the higher ranked player choose then a particularly dominant deck would remain dominant in that role).
If you then cut off to a KO bracket you can resume the traditional two game format.
What I think my method achieves is that everyone plays more different opponents which is good for social play. An individual game is worth 2 points (1 each for a timed draw), which means it's still possible to salvage a draw from a losing position in a game by stalling, but you can't transform that same position into a match win as you can with the current system.
In terms of logistics it needs a reasonably sized field to work successfully, but timing wise shouldn't be too much different to 5 rounds of regular play. You might need a bit extra time to account for extension turns in timed games (as these will impact the schedule more than in a two game format), but you have an extra half-match worth of time to use for this purpose.
[Edit was for formatting]