Will Canon EOS 5D Mark III body give me better photos than 60D body? (with same lens)

I'm not big in cameras but googling the 60D vs. the Canon brought up threads that mentioned "upgrading" to the 5D so I'm sure that's the better camera.

Of course. It is a full frame sensor compared to a APS-C.

However, you can't use all the lenses a 60D can.

Idk why people are still buying Canon APS dslrs though. They've been using the same sensor for years and all their new models are just rehashes. Nikon D7000/D7100, Pentax K-5 II >>>>

Can you explain your situation more?

I need a camera for my Photgraphy class but I don't know which one to get

They told me it has to be a semi-professional but my budget is around $350-750. I'm desperate

Now i own:

a EF-S 18-55mm f/3.5-5.6 IS II lens (can't use it with full-frame body, i will sell it and 60D body if i decide to buy a 5D Mark III body),

a EF 50mm f/1.4 USM lens (can use it with 5D Mark III body?)

a EF 70-200mm f/2.8 L USM lens (can use it with 5D Mark III body?)

a Speedlite Canon 430EX II (can use it with 5D Mark III body?)

Yes, you can use all EF lenses. Just not EF-S.

And I believe all Speedlite flashes are compatible on all Canon bodies.