Is there any benefit using weapons that use bullets vs energy weapons? Trying to play a sniper character with guns for close range and for some reason it just feels weird sniping with a energy weapons...

Is there any benefit using one vs the others?

Energy works really well against robotics and turrets so it's a good idea to always have one handy.

Different enemies are weaker and more resistant to different damage types be it ballistic or energy. Besides that, both weapon types also come with some weapon modifications unique to only them. Which ever one suits your fancy.

Most of the armor I've seen has higher ballistic DR than energy resistance, so more damage will get through. Plus, due to the inconsistent availability of pretty much ammunition type except for the stupid .38, it's important to diversify your arsenal. Plus, I found a great laser rifle that does 50% bonus damage to robots.