Take it from someone who have used both, both are excellent products. Each have its pro and cons. Herer is what I think Kaspersky excel;
a) Their heuristics. (Maybe your pure miss stuff because you didn't set heuristics to high. For any product I used, I always set the heuristics to high)
b) Their clean ability (not to say avast is bad, but I haven't tried the cleaning of avast. I have installed KIS on a heavily infected computer, it was able to install, update and clean without problem)
c)Kaspersky cloud is better than avast at the moment but this is the first time avast have cloud, so wait for it to improve.
d) Kaspersky have excellent self defense (based off malware research group. For two years in a row,(I think), it have receive the platinum award-the highest award)
Why I used avast?
1. Tried and tested. Was bought over by the detection rate. Tested some viruses bought back from school and saw Kaspersky and avast both detect the same thing.
2. avast have less bugs. (main reason why I switch)
3. Light on resources
4. It is free and very good
5. Fast (4.8 scan speed was like a snail. Now it is like a Ferrari
)
6. I like what avast is doing. (their ideas, their generosity)
I would like to used the paid avast if I can see a box avast for sale in stores in my country. All I see are Kaspersky, Norton, Trendmicro, Avira. Yet to see a box version for sale.