I usually use a travel agent for sight seeing holidays, reason being that they have agreements with certain hotel chains and know what is good and what to avoid, based on customer feedback. They also ensure that all your tickets etc. are correctly issued and that any mess ups are taken care of. For example, we were stuck in Bangkok due to the riots of 2010 and the travel agents phoned US and organised a new hotel. We didn't need to hassle in a foreign country trying to phone around. I found that you pay maybe a grand or two more, but for me that is worth it for piece of mind and quality.
But going DIY is also a good option - it depends on how confident you are. We do not book tours from here but find it much better to arrive in the place you want to visit and contact a local tour from your hotel or the internet. That way you aren't stuck on a bus for two weeks, but take day tours from central locations.
Also, do you own pricing research, then ask the Travel Agent to match or beat. We also get quotes from two travel agents and ask them to compete. It often results in a few grand off the price.
With passports and travel visas getting more complex, it's good to have an experienced person guide you - that way you will never end up deported from immigration and ruining your holiday.
Lastly, yes, be very careful of these cheap travel packages. As you saw, you can end up stuck on planes for nearly two days and sleeping in airport waiting areas. For a grand or two more you can get much better flights.