Returning to your original questions:
1) As shown in the figure, if I use both signal a and b to drive the same circuit that is also synchronised to 'clk', is 'a' more stable than 'b'? (Here stable I mean glitch-free)
2) How should I analysis timing for signal 'a'? I mean, for signal 'b', I've got a margin of roughly one clock cycle to accomodate combinatorial logic to avoid timing violation, but for signal 'a', do I only have half-clock cycle to play with if the signal that drives signal 'a' is synchronised to rising edge of the clock?
Given two circuits like this where the top circuit has a intermediate falling edge FF and the bottom circuit has a rising edge FF.
The timing paths associated with register A will require that the setup/hold time between InA to A and between A and OutA must be met for the circuit to operate correctly. This means in both cases the paths will have to meet a setup/hold with half the clock period available. (rising-to-falling and falling to rising)
For the bottom circuit the timing paths have the entire clock period to make timing for both InA to A and A to OutA. This circuit though will operate differently than the first circuit as it takes two clock cycles to get the equivalent output.
The first circuit could also be implemented as (removing the falling edge FF entirely):
In this case the circuit now combines the two combinational blobs into a single blob, that has to meet the setup/hold requirement between InA to OutA. This circuit is functionally identical to the circuit with the falling edge FF as the input and output will be the same between the circuits. As the circuits produce the same results there is absolutely no reason to add an additional negative edge pipeline FF in the path.
Note that none of these circuits are "glitchy". For any of these circuits to work they all must meet the setup/hold time of the FFs. Yes the combinational logic may have glitches prior to meeting the path setup/hold time, but during the FF capture window (from the start of the setup time to the end of the hold time) the input to the FF must be stable, otherwise the FF may go metastable (is this what you're thinking of when you say glicth?).
As FvM stated nicely in #10 FFs don't glitch. Though some older bipolar based logic families could produce runt pulses, but today's high speed CMOS logic this doesn't occur.