First of all a side note:
The angle of the blue lines isn't the same, as the tires have a certain cross section and shape. As soon as the bike is tilted, the point where it touches the ground moves out of the center line, into the tilt direction. In an extreme case, the bike could stay vertically, and only the driver tilts sidewards.
However, I see three reasons, why b) is safer:
While a) feels / is more stable as bike and driver are one unit, it needs more force to erect both into a vertical position. This force is not applied by the driver himself, as he can't erect the bike. Instead, he steers the front wheel deeper into the curve, which causes the whole unit to erect. At that moment, the force onto the ground increases, and the horizontal component may exceed the static friction.
In case of b), the bike is in a more vertical position and the driver can erect on his own. This causes less force onto the ground.
For almost the same reason, the driver can react faster when he sees that the condition of the street ahead changes, or may be, when the wheels already start to loose friction (which needs high skills).
As driver, you may imagine driving a curve very slow, once in the 'normal position', and once 'tilted'. 544
Imagine you manage to stop within 0.5m, because a ball is rolling on the street or similar. It's quite impossible to erect from the 'normal' into the vertical position, while it shouldn't be a problem from the 'tilted' position.
Another reason is additional torque on the tires. The surface of the tire which touches the ground has the size of... may be an egg. In a curve, the inner and outer side of this surface have a slightly different speed over ground, while the speed of an upright wheel is the same. This difference has to be compensated by the rubber of the tire, and creates a torque around the vertical axis.
For a certain angle of the wheel, this torque can be canceled out, as the inner side of the surface touches a point of the tire, where the wheel radius is lower. However, this usually happens at a fairly small angle, and with increasing angle, torque increases into the opposite direction. And of course, this torque should not exceed the static friction.
So, even in this case, b) is safer, as this torque is lower. 544