Here's my story:
One of my former clients (who has since moved into a partnership with two other people & have a full time office staff) used one of the services you mentioned (I won't name which one). They didn't comprehend that there were certain ways you had to do things here.
He's local to me, I met him at a networking event, and he had just had a really bad experience with them, and he spent most of the time talking to me about his issues. He told me how much he paid for what he got and I thought, at the time, there's no way to compete with that. Monetarily - if someone's watching the bottom line - you can't. But how you can compete is through SERVICE.
Skip ahead 3-4 weeks, I get a frantic call from him (he was not my client at the time). He's flying from Michigan to California to meet with several people. He's a real estate investment advisor, so he meets with people with M.O.N.E.Y. and its very important that things go a certain way.
This overseas VA company had done the following:
1. Only allowed him one hour between appointments, in other words: Appointment with Mr. Smith at 10:00 a.m.; appointment with Mr. Jones at 11:00 a.m. And the problem is: Smith and Jones' offices were an hour apart! Leaving no time for travel!!
2. Had scheduled his last meeting almost 2 hours away from the airport, an hour before his flight was to take off.
3. And that last meeting was with people that had major M.O.N.E.Y.
Client called me from the airport in Phoenix, clearly distressed. Now remember - he had only met me once. We had talked for about 30-40 minutes, tops, and had exchanged emails a couple of times after that. We had no client-VA relationship at all, hadn't even talked about it, really. He called me because he was trying to start his company on his own, watch his money, and had no support. He had my business card in his pocket from meeting me weeks previous.
So I asked that he fax me all of his paperwork - itinerary, phone numbers, anything he had and I told him I'd do what I could to straighten things out.
Already long story short: I got all of his meetings fixed & organized the way they need to be. Got him on another flight (which ended up being direct, rather than 2 stops), so he got back home earlier.
And I did not charge him for this. He did send me a really wonderful gift basket from Ghiradelli chocolate, and he refers anyone and everyone to me that he meets that could use a VA.
We ended up working together for about 6 months until his company was merged with another, and they put an office staff in place. I still see him (and his partners) at functions, and he introduces me as his "Life Saver".
So - no, you can't compete with the cheap prices, but you CAN compete with the service.