|Figure 1: The Colonel adds to the Party's Initiative roll|
Multiple instances of Initiative stack, so it is an ability which can weigh the odds of winning the Initiative roll in a player's favour. While I don't suggest picking a Party to win just one roll each Turn, when faced with some choices of unit, it may be a factor to weigh up.
Figure 1: For example, The Colonel has Initiative. If playing him, then the Tactical Advantage Plot Advantage Card is worth consideration as it also adds +1 to your Initiative roll. Doubling up the bonus means that the odds significantly shift in your favour (around 64% of winning/74% chance of not losing - assuming no extra dice etc. - if my maths serves me well), which can be useful tactically and psychologically (will your opponent burn a Gnosis point for the increased chance to win the roll?). Again, it is not the be all end all strategy, but something to think about.
Azur have the most easily-combined options for Initiative, followed by Church, Empire and Wissenschaft; In terms of synergies for Party-building, I would suggest that Azur have the better options, which helps compensate their relative fragility.