We have a high proportion of onshore on-site Indian employees who are absolutely awesome. However they've gone through the local company's recruitment process so will have been selected for fit.
The experience with outsourced resources is significantly different.
I build a good rapport with one who talked me through the politics and power plays behind the scenes at their midsize outsourcing arm. Just very different social values to Western orgs. Incredibly hierarchical with no value given to autonomy or independence. Those who want to do well and try really hard frequently get their helmets dented by over zealous managers.
Also experienced - ex offshore very often have incredible cvs until you interview and there's no actual experience. Polling the above contact he mentioned that for some offshore orgs promotion is literally time in role, not competency based.
My experience, your mileage may vary, and I reiterate those I've worked with on-site have been awesome, generous, funny and very supportive people.