Once I tried concentrating DNA by Speed-Vac and found it somewhat degraded (not very confident whether it was because of heat of speed-vac or some external contamination because I did it only once). Although some DNA is lost during ethanol precipitation, the quality remains good.
As long as it's dry, it will be very stable. Shouldn't matter too much how you get it to be dry. It's possible to damage it during drying, if you have chemicals, like non-volatile acids or bases in the mix. Even traces of non-volatiles will become extremely concentrated during drying, as the volume goes to zero.
So that's what the freeze-drying does for you -- when it evaporates from the frozen state, the molecules don't move around as much, and don't "see" the greatly increased local concentrations you would get in a liquid. You can achieve that both in a speedvac or in a lyo. Doesn't really matter. The lyo just makes nicer fluffy "cake" structures, if you have lots of material (and optimize everything in excruciating detail).
My favorite method is to spot the DNA on filter paper and just let it sit there to dry at ambient temperature.