Its 6 of one ... and half a dozen of the other isn't it?
1) Make deep planting holes, fill with prepared compost, station sow 3 seeds each
Pros: less effort than paper-pot method
Cons: weeds will compete from day one, if germination is spotty resowing is likely to be pretty late; need to have the bed prepared, and be able to get on the soil, early in the season (on my clay soil, and given my bone-idleness early in the year! that's "unlikely" in my case, and a major deciding-factor for me personally)
2) Prepare deep paper pots, sow seed per-pot, or chit first; plant out as soon as first true leaf appears
Pros: One plant per station, no gaps; later soil preparation(**); less weed competition
Cons: time and effort of making paper pots, watering an nurturing; needs conservatory / greenhouse or similar "space" for raising the plants.
(**) I sowed my newspaper pots on 11-Mar and planted out on 11-Apr, so it "gained" me a month.
Both (assuming you make tall paper pots) provide 8" or so of good soil to grow in, and incur similar cost for compost etc.
3) sow direct.
Pros: avoids the cost of compost, and considerable time saved on faffing around and nurturing. Great method if soil is already in good heart.
Cons: spacing may be erratic / gap-y; other factors as per (1) above. Needs time to make a decent seed bed (dunno how the various methods compare in terms of "minutes / parsnip produced!) and extra early-season weeding.
It occurs to me that for outdoor-direct-sowing and if quality of seed is uncertain, or even just "to be more certain", then a few seeds could be chitted a couple of weeks before the actual outdoor sowing to check that germination percentage is high.