They aren't supposed to use much if any Naquada in their construction.
It's generally assumed the style of gate from Destiny is oldest but some sources, namely the comic continuation of SG:U indicates Destiny was launched well after the era we see Atlantis leave Earth on screen. The comic is supposed to be a canon continuity but the publisher made tons of typos in the equally "canon" SG:A comic. So who knows.
The design differences could be for reliability
It's worth considering that the two main failure modes we see for MW gates are the inner ring getting stuck and the gate falling over. It's a very bad day for any traveler who comes through after the destination gate has fallen on it's back... We see the Pegasus gates eliminate the inner ring but it seems the only thing keeping these gates upright is the fact everyone seems to know how to use them and its also in their best interests not to make the Wraith come in ships. However the Ancients were clearly expecting to be around to maintain them.
In SG:U the gates also eliminate the inner ring but preserve manual dialing. This could be an alternative approach used by a design competing with the Pegasus model. Explorers far from support and rescue are much more likely to need it especially after the gates are left unattended for perhaps a million years. Likewise the fact these gates are fixed in a large base could be the obvious way of reducing the chance of falling over and this only makes them seem less advanced.
They might have known naquada was very rare in most galaxies
Even the reduced or eliminated use of naquada might only reflect the fact they never discovered it until they were in the Milky Way. Meaning they might've had good reason to expect it's not always as plentiful and therefore should not be used as a necessary constituent of the seedships gates. This seems most likely but doesn't require these gates to be newest or first.
Presumably these gates are only expected to last long enough to support Destiny and it's crew in their mission. I suspect Destiny held at a fixed point for an unknown time waiting for it's overdue crew to gate in. If so there could be quite a gap between it and it's fleet of seedships. We know at least the gates near the Norvus colonies were there at least 2,000 years but this is only a lower limit for how long these gates are known to remain functional.