I would use a travel agent for a long haul flight. I would feel happier having someone to contact if anything goes wrong.
Having said that, for our 3rd trip to the US, we could have done everything ourselves. On previous occasions, the travel agent had organised us a hire car and road trip but with far too much driving. We wanted to drive shorter distances and look at more sights on the way.
I worked out an itinerary and asked them to book hotels to fit. I had planned a sort of John Steinbeck tour, so I included Salinas and Monterey (California).
When I got the bumph back, I made myself a little booklet to cover the itinerary including overnight stays and discovered that she had booked us a hotel in Monterrey (Mexico) instead of Monterey in CA.
So even if you do use a travel agent, check everything twice. Check the date, in particular,including the year!