Both of your sentences are completely correct. Although you can use either see/witness, witness is more formal and generally for bigger or unusual events. For example, you could say both of these sentences and they would mean the same thing: "I witnessed a crime yesterday" or "I saw a crime yesterday". However it would sound very odd to say "I witnessed a film" because watching a film is quite common. I this case it would definitely be better to say "I saw a film" or "I watched a film" would work too :) I hope this helps!