I make a big title. But what I'm going to share is only my experience in getting tourist visa from both countries. I did it almost the same time--applied for Indian visa and then Chinese one.
India just introduced a new E-Visa system. But it's for one month's stay only. Since I need to stay in India longer, I have to apply for visa in the old way.
Regarding China, there's online information about 144-hour visa-free visit in Guangdong province. I booked my flight ticket after I saw such information, thinking of making use of such policy. However, later when I tried to find more information about that, I read text like this: There is such a policy, but it has not been implemented yet. I was totally shocked. I don't have much time, so I had to rush to apply for a Chinese visa.
Both countries require information of previous visa. India only asks you to provide the visa serial number, but China requires photocopies of previous passport and previous visa.
The visa application services are outsourced to agencies, both India and China. So what I actually dealt with were the agencies.
After I mailed my application kit to BLS, the Indian visa agency, I read news about the upcoming solar eclipse. I decided to drive to Oregon to view it, but my passport had been sent to BLS. I made several phone calls to them trying to get my passport back before my trip to Oregon. The agents answering the phone were polite. However, some had stronger accent. There was quite a high level of noise in the phone too, I could here talking of other agents. These made the telephone communication a bit difficult. Eventually I was able to get my passport back for my eclipse trip.
After my eclipse trip, I sent the application kit to BLS again and got the visa several days later.
For the Chinese visa, I went to the visa centre's Vancouver office in person. There's an online system to book appointment, which makes the wait time much shorter. The receptionist was polite and professional, I got a ticket from him and waited for meeting the agent.
The agent didn't appear friendly to me. He picked on my photo, saying it's of low resolution, not enough contrast, and not recent enough. Actually the same photo was used for the India visa. I was well prepared--I brought another two versions of passport photos. I gave him another photo. He was still very critical, I had to explain to him over and over. The photo quality was even better than the one currently on my passport, I had to point it out to him. Eventually he reluctantly accepted the photo, but still warned me that the consulate may reject it.
He then picked on another thing. The old passport I brought was not the most recent passport, he was not happy about that and questioned me a lot. This was not really a documented requirement though. Finally he told me to print a note, using their office computer, to explain the reason. They charged for the printing.
At this point, I felt that the Indian visa agents were someone who were there to provide services, while the Chinese agent just reminded me the red tape in China. I had been worrying about my Chinese visa application because of what the Chinese agent said.
A few days later I went to the Chinese visa centre again to pay fees and pick up my passport. Luckily this time the agent was very polite. I got my passport back without incident.