I have both negative and positive things about close in age gaps and large age gaps. I am the youngest of 5. My oldest sister is 12 years older than me and was out of the house in college before I was 7. I didn't know for the longest time that she was even my sister because she was never home when I was young. Now we are very close, but I feel like I missed out on growing up with her. When your older the age gap doesn't seem to matter as much.
Now my sister that is only two years older than me is another story. As kids and teens, we fought a lot but also had good times together. I think because we were close in age, we competed against each other for attention, friends, etc. I was always in her shadow in highschool which was difficult at times.
You didn't say whether your third child was a boy or a girl which I think will make a big difference regarding their age gap. I personally feel if your third is a girl, you won't have any problems with the gap. If the third is a boy, you might. What 10 - 13 year old is going to want to play with a 3 year old. Girls are different. They will want to play mommy to the little one or play games.
If he is really concerned, you could always have a fourth so the two younger ones are close..lol