In practice, there are two main reasons to stick with the exchange: for many people it is cheaper (because of subsidies), and for most people it is simpler (because you can see many plans in one place in a standardized way instead of having to visit many different insurer websites).
For most people, the biggest advantage of buying plans from the exchange is the potential for the premium subsidies. You can't receive subsidies if you buy a plan off the exchange; you have to pay the entire cost yourself.
If your income is too high to qualify for subsidies, that advantage is moot for you. The exchange does offer some other advantages, such as the ability to directly compare plans from different insurance companies in a standardized way. If you shop among insurance companies "manually" you will have to do this comparison yourself.
In theory, the idea is that the exchanges will be able to negotiate better rates by offering insurers the opportunity to easily reach a large pool of customers and federal money (the subsidies). It is still too early in the adoption to know for sure whether this will be the case in the long run, but I found at least one analysis according to which the cheapest on-exchange plans are usually cheaper than the cheapest off-exchange plans.
As for why companies might choose to offer plans off the exchange, as I understand it the main reason is simplicity. Although the plans themselves must still meet the legal minimum coverage requirements, the process of joining an exchange involves a series of negotiations between the insurance company and the exchange. These negotiations may deal with not only the level of coverage but also the cost (as divided among the "metal tiers") and the doctor network. If insurers don't join the exchange, they don't have to engage in this process, and can essentially set their plan up any way they like, as long as it meets the legal minimums.
If you google around for "off-exchange plans" you can find various articles discussing reasons for looking off-exchange. I found some such articles, here, here and here. (As with most writing about Obamacare, it is wise to read such material critically and with an eye to the source.)