I have built many balustrades yet never with round balusters. I usually use 35x35 square and make a decorative groove on each side and router off the edges stopping 150mm short of the end in each case.
You need a router table to do this.
I make a groove with the router top and bottom rail because it is much easier to get the distance between the balusters and keeping everything vertical that way. I use one skew nail (small) because I also use spacers/infill between the balusters. A strip of wood that fills the groove exactly flat with the sides of the rail and doubles up as spacer. The nail is not even necessary. I however glue and nail the spacers. This is of course a bit laborious. If I had to do this with round balusters ... mm. Well I wouldn't but if you are set to use round stuff, 25 mm seems to me to be on the small side. You could still use the above method but would need to square off at least two sides of the dowel to allow for the spacers. This would make the stairs balustrade easier (not easy)
To do it drilling the holes is in principle easier but in practice difficult because of the precision you need in the drilling and the unforgiving result if you have a dowel out of plumb or not exactly spaced. You could make a jig for it and also for the stairs balustrade, that includes a spacer and a guide for the spade drill. Actually perhaps a forstener bit would be a better choice. In my opinion ... forget it. Go for square balusters.