No, they were the best armies because they were trained to European standards, which made them far more disciplined in battle. Indians believed European troops had near magical qualities in their ability to withstand fire and survive. The earliest armies were European troops - people not good enough for the British army often joined that of the EIC. They then recruited Indian troops as they got more involved in local affairs. Sometimes this was from controlled territory - sometimes it was just recruiting Indians from next door. The French had a decent sized Indian chunk of their company army, and they never had major territorial concessions.
The other advantage the Europeans had in the early days was their navies. The battles were close to the coast, and the Europeans could remove their army if it was going to lose, or reinforce one that had the potential to win.