There are a lot of different blockchains afterall e.g. nem, ethereum, neo, QTUM and bitcoin blockchain, just to name a few. Do they together benefit from having more people using, so that the total 'blockchain-network', so to say, becomes bigger?
They benefit from each other in that they share an economy that functions independently of traditional banking systems. So while we currently have to mostly rely on centralized entities such as exchanges to trade crypto-currencies and tokens for one another, this may enable a decentralized global market place further down the road.
What is the technical overlaps of different blockchains, and how do they complement each other?
Technical overlaps depends on what you mean. Many alts technically overlap in that they are forks of the Bitcoin codebase. Many alts overlap on a higher level in that they reach consensus via proof of work. I'm sure some other members have additions to make.
Roughly I guess you could break it down into 2 kind of blockchains: 1) currencies and 2) utility tokens.
Currencies may have various properties that may benefit one use cases over the other. Some currencies may be better as store of value, some may have better privacy properties.
Utility tokens usually act either as a kind of security / stock or as a way to use the service of a decentralized application in the broadest sense of the word.
