op-amps: where to split the rail?
You have a rather weak connection to the midpoint voltage. (50kΩ.)  In the first circuit this is fine, but in the second it is not.  The midpoint voltage will drift a lot, because the load current is being returned through the same 50kΩ impedance.  You even get coupling from output back to input through the Rload to the bottom of the input voltage.  This can cause oscillations, though probably not for a Av=1 buffer like you have here.

My suggestions:


If you want to AC-couple input and output, use circuit 1.  Circuit 2 gives no advantage.
If you want to avoid AC-coupling, use a rail-splitter circuit (e.g. buffer the midpoint voltage with another op-amp.) Then you can dispense with the caps because you have a good +/- 4.5V supply.