Give birth in Kathmandu, best hospital

First, congratulations and very best wishes.
Having never had children in Nepal, I defer to others who have, but what you may want to do is seek advice from a doctor whom I happened to go to for something else. I think very highly of this Doctor. Although his specialty happens to be that of a urosurgeon, I think you will find to be most helpful, and no doubt he can refer you as he thinks is appropriate.  His name is Dr. Parash Mani Shrestha and he is associated with Blue Cross Hospital in Tripura Marg, just behind the football stadium in central Kathmandu.
If you'll check this hospital's web site, they are pretty straightforward in their candid assessment of the conditions here when they write that Nepal is a developing country and the Government alone cannot provide health care with standard and modern diagnostic and treatment facilities of all conditions to the population. And they readily acknowledge the fact that existing hospitals, even in the capital, lack adequate, modern, up-to-date, hi-tech and expensive equipment and treatment facilities. Hence hospitals are coming up from the the private sector to fill in the gap etc. as they go on to explain all of that. 
Like you intimated, and that is correct, this will explain why most of the expats in Nepal will not hesitate to seek medical care or treatment in ultra-modern hospitals abroad, notably in Bangkok, Thailand. And the first name that comes to mind there is of course the Bumrungrad International Hospital (named Top 10 world medical destinations)
See what Dr. Shrestha says, and decide accordingly. No doubt, you'll make the right choice!