My wife and I have just completed 4 domestic Myanmar flights booked through OWAY. The website may look like it's in the 21st century, but there are some substantial downsides in relying on that first impression.

Pros:
Calls to the California based 800 number are responded to promptly
Payment by credit card is available, thereby making life considerably simpler (for those not use to carrying lots of cash)
Flight tickets are delivered to your hotel upon arrival in Myanmar

Cons:
Flight purchases are not, ultimately, for the flights that you choose on the website. Of our four flights recently completed, only one was the same airline and flight number that we thought we were purchasing.
OWAY is not acting as an agent in the traditional OTA model, where the credit card charge is by the ticketing airline ---- your credit card is charged by OWAY LLC, and the charge is not recognizable as a travel expense (i.e OWAY is not registered as a travel company by Visa, Mastercard etc).
OWAY's support staff are inexperienced and sometimes extremely unhelpful. For example, we were informed definitively by OWAY that two of our flights were not operating because the Bagan airport would be closed for a 3-week period and that we needed to find alternative means of transportation. This turned out to be idiotically poor information (the airport was closed on certain afternoons for renovations).
On 3 occasions OWAY changed our airline and flight times without any advance consultation. Emails to them requesting alternatives went unanswered / unresponded to. [Fortunately the airlines themselves are extremely flexible and our travel plans were modified without OWAY's assistance].

All in all, I think that OWAY's best attribute, it's website, is also it's worst. Anyone who uses the website to carefully choose which airline and which flight time they wish to purchase will probably be extremely annoyed to find that their issued tickets are for different airlines, that nonstop flights are now multi-stop ones, that departure/arrival times are now inconvenient, and that refunds for such changes are neither offered nor forthcoming. YMMV