I am the same as Simon (or was, I have a WFP now) I have a variety of different sized squeegee's and a small applicator.
A damp scrim and dry scrim can work really well on the right type of work, but the bigger the pane of glass the harder it gets.
On larger panes the squeegee will always beat the other method.
On some georgian windows I even use just a sprayer, mist the glass and squeegee off with appropriate sized squeegee. In my sprayer I always use a solution of Car Plan windscreen washer fluid (10:1 mix) It's cheap, £2.50 for 5L and it does a great job with the squeegee or lightly misting and buffing with a scrim.
Experiment, try lots of different things, be adaptable, I've been going 20 years and I'm always trying different ways to tweak and improve, make things easier, cheaper, more efficient and so on.
One other point re-squeegee V scrim; It takes several months of constant daily use before you get to be really profficient with a squeegee.
When you are really starting to get there you will only need a maximum of 3 or 4 scrims a day, and one of those will be your wet one, used for mopping up & wiping down sills and so on.
Ian