There were indeed two (or three) Plymouth bus wars.
The first was as you say in 1988. There had been a local industrial dispute in Citybus with an all out stoppage and this emboldened Western National to expand their presence on city services; they had historically operated services in the city as part of the joint services agreement IIRC. At that time, Western National were owned by Plympton Coachlines though it was an open secret that Badgerline had a shareholding in the enterprise, and whilst the bus war was ongoing, took a majority shareholding. The Citybus drivers went back to work and after some more competition, peace came about but as you say, WN did probably get the better of the deal in the end.
Then in 2008, Plymouth City Council decided that they would look to sell Citybus. First went in all guns blazing with a landgrab with their Ugobus network featuring nearly new vehicles drafted in from West Yorkshire, Glasgow, Manchester, some older ex Bristol B6s and some ex Hong Kong Darts. Unfortunately for First, the council sold to Go Ahead who had much deeper pockets; that and the fact that First had really gone off half cocked. First lost millions on the escapade, so even when peace came, the losses continued.
By 2012, the position hadn't improved and Tim O'Toole then publicly declared that South Devon was in close down mode. The tables turned, Go Ahead then decided to make a pre-emptive strike to secure a better position in case of a sale with services to Torpoint and Tavistock plus additional services in the city. First battened down the hatches, moving the most expensive vehicles (e400) to Cornwall for the U1/U2, replaced by elderly Tridents. Similarly, the only other "modern" single decks (other than the odd Dart or Solo) were some 2001/2 B6s that were sent to Somerset. They were then swapped for some Somerset B7Ls and a few more ex Bristol B6s (which were very peachy by that time), in readiness for the sale to Stagecoach. As part of that sale and subsequent de-escalation, Citybus retained the Torpoint route (with the First depot closing) and out to Callington so in a reversal of the first one, Citybus probably got the better of things of that war.