I think they're exactly the same technically, the only differences are in the characters.

Mortal Kombat Deadly Alliance had Li Mei, Sonya, Scorpion, Kenshi, Kung Lao, Frost, Jax, Shang Tsung, Quan Chi, Sub-Zero, Kano, and Kitana.

Mortal Kombat Tournament Edition had Shang Tsung, Bo' Rai Cho, Quan Chi, Scorpion, Johnny Cage, Raiden, Sareena, Nitara, Mavado, Hsu Hao, Reptile, Cyrax, Drahmin, Noob Saibot, and Sektor.

The games look graphically identical.
The Deadly Alliance version only has twelve characters, while Tournament Edition has 15 (with one random select spot.)
I'm not sure if both versions had survival mode, though.
Also, I think only Tournament Edition had the secondary weapon fatalities. I'm not 100% sure, though.