OTA's are not travel agents, they are electronic ticketers. If something goes wrong their reputation is terrible, and there are plenty of bad stories in this forum and elsewhere that bears it out.

When I first started looking into this I found that actually while BA's website wasn't too good at the relevant patching together of complex fares, BA's booking agents can generally match or improve on Orbitz's price. Orbitz doesn't get a commission for selling BA flights, it builds in a fee to the price you see online. Therefore BA agents are often - not always - able to undercut these fares. It needs good usage of ITA Matrix and ExpertFlyer to ferret out the details. The key thing to watch is Point of Sale: Orbitz exploits this to the n'th degree, whereas BA online does not.

E.g. recent FUE-MAD-LHR service about 3 weeks back, mixed IB and BA. BA.com didn't price up (IB starter when there are direct BA flights), IB came up with 100€ or something similar. Orbitiz, via Skyscanner had 82.45€. BA was 68.44€ which I got priced into sterling at £52.88 on the day in question. I have not in recent times found an example where the OTA could beat a BA price, and given the price guarantee that BA offer in most jurisdictions, that is what you would expect.

[One exception is where AB have multiple sectors falling into a final BA sector. I haven't found a reliable way of beating OTAs here].

So in essence I don't see the point in paying more for less service.