You are quite right that new turf (roll out lawn) may look different. Is there any way you can divide the two areas: eg with a path or border so that it is not so noticeable? You could take a typical piece of the old lawn to a supplier to analyse the mixture of grass types as they may have more than one mixture available. You can still get the same problem with seeding.
Seed grown lawns do establish fairly quickly if sown when the soil is warm and moist, but you must give it a bit of TLC and not let it dry out in the summer or let animals / kids attack it.
One problem with seeding is that weed and grass seeds already present in the soil will germinate among the new seed. Preparing the soil tends to bring buried seeds to the surface.This can be a real problem if docks, nettles, dandelions, daisies etc are present.
As long as the drainage is ok, don't cultivate the soil too deeply or it may settle out unevenly after you've sown the grass. 6 ins is plenty and incorporate something like Brown Gold or even potting compost.
I would do this now, lightly tread and rake it, removing large stones, roots etc, then water it and leave it for 3/4 weeks. It will settle so you can see any adjustments you need to make and the weed seeds will germinate.
When they are growing strongly but before they get too big, spray them with Roundup to kill all off and it will give you a clean surface for sowing. (the Roundup won't affect your seed later.)
Then lightly rake over and remove dead material and sow your seed. Don't skimp on the seed - it's quite a big area so try and find somewhere you can buy a sack if possible rather than small bags or boxes.
It will take 2/3 seasons before it's comparable to a rolled out lawn for thickness.
Good luck.