I have been doing web design & development for about 13 years now. I have built websites for fortune 500 companies, SMB's and local mom & pop shops, chabad houses etc.
I have done lots of work overseas (India, Macedonia, China, Ukraine, Russia & Finland) and had lots of ups and downs. I have had to fly to some of those countries to whip the team into shape etc....
Overall I would say stick with a local reputable firm for anything above an info site. Its a known fact that Indians suck at design as well.
Ukraine is good for eCommerce or custom stuff like CRMs etc.