Typically the base damage on a 2-hander/dual wield setup will be about 20% higher than that of a 1h/shield combo. Two-handed skills will frequently deal equal or better base damage (further amplified by the higher base weapon damage) in the situations in which they meant to be used than similar 1h and shield skills. Two-weapon skills typically have lower base damage per hit, but make up for it with more hits.

Survival tends to increase with greater damage in small encounters (two to three opponents) even over using shield, especially if you can keep them CCed. In larger encounters (typically only found in dungeons) you'll suffer a bit if you rush in without adequate protection.

Two-handed and dual wield tend to deal greater single target damage than a destruction staff, but far less area damage. This is further amplified if you specced heavily into Ardent Flame.

I will warn you that unless you are wearing light armor with several of the perks, have a lot of magicka through enchantments or level up points, and/or are a High Elf/Breton you may have difficulty with sustained magicka cost for restoration staff skills.