The level 20 ability entry reads:
"Lich Transformation: When a dread necromancer attains 20th level, she undergoes a hideous transformation and becomes a lich. Her type changes to undead, and she gains all the traits of the undead (see page 317 of the Monster Manual). She no longer has a Constitution score, all her existing Hit Dice become d12s, and she must reroll her hit points. A dread necromancer need not pay experience points or gold to create her phylactery."
MM p.317 has the information on the Undead type.
MM p.167 has the info on a Lich. In addition to Undead traits, a Lich gains a +5 to natural AC, gains a 1d8+5 touch attack of negative energy, a paralyzing touch, a fear aura, a +4 turn resistance, DR 15/bludgeoning and magic, Immunity to cold, Electricity and polymorphing, +2 Wis, Int and Cha, and some skill bonuses.
Pre-level 20, the Dread Necromancer gains DR up to 8/Bludgeoning and Magic, Light Fortification up to 50%, a negative energy damage 1d8+(1 every 4 class levels), up to 4/day a negative energy burst that deal 1d4/class level negative energy damage that harms living and heals undead, up to +4 resistance to sleep, stunning, paralysis, poison and disease, a fear aura, an up to 3/day disease touch attack, +4 bonus on saves to resist negative energy effects and Bestow up to total class level negative levels to a target as a touch attack each day (no more than 2 levels with each touch, able to use Spectral Hand spell to touch negative levels at a distance). The Dread Necromancer also gains class abilities that make it incredibly powerful at creating a small undead army on a consistent basis.
With all this said, comparing the Lich Template to all the cumulative abilities the Dread Necromancer receives just by reaching 20, The Dread Necro is quite a bit more powerful on offensive abilities (Negative levels, disease touch) and a little less powerful in defensive abilities (no natural armor bonus, DR8 instead of DR15), but does gain the 50% resistance to crits, as well as a different set of immunities than the Lich template.
I personally would rule that, upon gaining level 20, the Dread Necro gains all the Undead traits and details as stated in the Lich Transformation entry for the class, gains the free phylactery, and does NOT gain the other aspects of the Lich Template, because they are simply a slightly different kind of Lich. The Dread Necromancer is an offensive undead, Able to drop a target 20 levels within 10 rounds at a distance with the assistance of a level 2 spell! Turn out some undead to keep those pesky opponents at bay for a few rounds, than drop an entire party of 4 adventurers 5 levels each, if you so desire, from behind your undead bodyguards. Use your ability to inflict negative energy to heal your own undead, and yourself, at 5hp a round, or if those opponents break through your bodyguards, do 4 bursts of 20d4 negative energy damage in 4 rounds. And add the ability to spontaneously cast from a decently powerful list of offensive, battlefield control and debuffing spells.
I think the offensive power offsets not having an extra +5 AC and 7 more points of DR.