If I am a dual citizen do I need to travel on both passports?

[ChabadKahanist]

Or do I only need both passports traveling to the Us & back to Israel in other words if I travel anywhere besides the US is one passport my Israeli passport sufficient?

[Hrvatski Noahid]

I have one passport stating I am a dual citizen of the Republic of Croatia and the European Union.

One passport should be sufficient.

[Zelhar]

I think you should generally take both passports as precaution. To travel out and in Israel you must carry your Israeli passport and I am pretty sure the same applies to your American passport for travel in/out the USA.
If you don't travel through the USA I think you don't have to use your American passport but depending on the destination it may be easier to use it (visa waivers etc.).
Some countries are easier to enter with Israeli passport. I think Russia and probably the rest of the former USSR for example, where Israelis don't need visa. Maybe Also countries in south America like Argentina.

[ChabadKahanist]

I think you should generally take both passports as precaution. To travel out and in Israel you must carry your Israeli passport and I am pretty sure the same applies to your American passport for travel in/out the USA.
If you don't travel through the USA I think you don't have to use your American passport but depending on the destination it may be easier to use it (visa waivers etc.).
Some countries are easier to enter with Israeli passport. I think Russia and probably the rest of the former USSR for example, where Israelis don't need visa. Maybe Also countries in south America like Argentina.

I was planning on maybe visting Europe

[Hrvatski Noahid]

I was planning on maybe visting Europe

If you visit Croatia, let me know so we can meet.