Petroleum Engineering:Petroleum engineering deals with upstream. Upstream involves exploration and production.Major areas are drilling , reservoiur production, formation evaluation and exploration of oil and gas.If you like dealing with geology and underground formations and you have some prsonal toughness then one can go for petroleum.

Petrochemical Engineering:Petrochemical engineer  deals with downstream. The principal end use products are plastics and resins,synthetic fibres, detergents solvents,paint varnishes,etc.Downstream involves refining.If you are interested in plant site, working on a balanced team to make the plant more profitable, and you have strong attention to detail then go petrochemical.