I don't think your question can be answered high level - you'd have to provide more details on what you try to achieve. Some questions which jump in my mind:
what do you mean by "connect"?
- Ethernet? (e.g. via USB dongle) - works fine
- WiFi? works fine
- WiFi direkt? -> should work as well
- Bluetooth 2.1?
- various protocols supported (e.g. RFCOMM, probably also PAN)
- Bluetooth LE?
- also several protocols should be supported
- will both Edisons be on the same network?
- will both Edisons be connected to the internet?
- peer to peer connection or broadcasting?
- SW wise:
- on Arduino or on the underlying Linux?
- e.g. Bluetooth RFCOMM should work
- scp? works fine
- sftp? should work as well
- nfs mount? (haven't tried on E yet)
- sshfs mount? (haven't tried on E yet)
- ipv6 (my preference if supported by hardware like router ...)
- websockets? - work fine
- via in between server / Cloud (e.g. RESTful API) -> allows data exchange also for Edisons in various networks
what do you mean by "send data"?
- what kind of data?
- amount of data?
- reliable / unreliable? (e.g. if you have to decide between TCP, or UDP respectively)
- singular data exchange or continuously?
- unidirectional or bidirectional?
- is it only about moving over data or about producer/consumer pattern?
- asynchronously or synchronously?
what latency do you expect?