If anything this shows why the Southern Approach to Heathrow (rail) should be built, in that there's demand for a coach link from both Guildford and Woking.
Although I'm all for competition, so I also hope that the coaches do well too.
Lets not be too hasty, you say "demand from both Guildford & Woking", Woking is @ 7 miles from Guildford, there's a train every 15 minutes during the day, the journey takes 10 mins.
Up to now if I want to get to Heathrow, I buy a single combined through ticket (train & Nat Express coach from Guildford to Heathrow, 10 mins to Woking, @ 45 mins (longer, depending on the time of day)
Total time with waiting and connections @1hr 5mins (you always get an earlier coach than you need to because of possible congestion/delays).
New First service timed at 1hr 5 mins direct with no change(via Surrey University).
The Woking Nat' Express Coach service frequency was reduced from every 30 mins down to every hour a few years ago, making the service less attractive, although probably more profitable for N.E.
Of course only a small number of people currently using N.Express originate in Guildford, many travel on the main (South West)line into Woking and anyone travelling up on the Portsmouth route, has no incentive to get off at Guildford rather than Woking. Presumably First are hoping to 'Grow' the market.
I don't know what the price difference between the 2 coach services is going to be, would have to be a big difference in Surrey.
As I and others have already commented, congestion and delays are the real issue here, My fall back has always been, If the Motorway is closed/Gridlocked and you are desperate to make a flight, you are 7 miles closer to Heathrow and and there is a plentiful supply of taxis at Woking and I know every route/back road to heathrow even if the taxi driver doesn't!