High side emitter followers are generally not recommended for relay drivers for various reasons:
1) The base drive voltage threshold is generally quite high, almost near to the rails. This doesn't leave much headroom and some relays may not ever pull in with the voltage drop Vce in play.
2) high side emitter follower's turns the relay into a voltage threshold detector. i.e. the relay will turn on when the base voltage reaches some threshold V
t(on) and this can vary between relays... which not so good for production... and given #1 above you may not even be able to reach the necessary V
t(on)3) Because relays have a much lower holding current than their pull-in current, it introduces some hysteresis into the relay's turn on and turn off voltage (+1V
be again at the driver's base). This can make it difficult to cause the relay to turn off when you want it to, since you have to bring the base down below the voltage that causes the necessary holding current
Low side NPN drivers sinking current to ground are always going to be better. They have near 0 hysteresis, it does not change the voltage threshold as seen by the relay (which always sees the rail voltage, so it always has enough voltage to turn on) and they are always happy turn off when told to.
And my opinion is that you always need the diode across the relay, whether you use a high-side or low-side driver. I'd rather use a beefy diode as close to the relay terminals as possible, rather than introduce trace/path inductance to the transistor, and then relying on the somewhat fragile transistor to withstand these transients. Vbe can easily exceed 100V for that fraction of a second until it turns on and limits the voltage to 0.6V , and many small signal transistors can't take that abuse for very long. Finally, if the transistor is turned on during the flyback time, then it can have current flowing from collector to emitter again just near the point of the 2nd turnoff event, and then you can get relay chatter. It's so much better to just use a proper diode at the relay coil and give the current the ability to dissipate within the coil resistance itself as the magnetic field collapses.
Finally: relays are old school for voltage taps now. Dom0 said it already here:
Consider using thyristors and opto-thyristors to 'extend' a bridge rectifier. I consider relays mostly obsolete for this application.

Put your full-bridge rectifier at the output. An alternative design uses the SCR's seen in the drawing as one leg of the bridge rectifier.