Selecting which one to use might be a problem, because each of them has its own advantages and disadvantages:
For wired connection:
+ Relatively cheaper than wireless router
+ Efficient if used on a big network (usually are used on an office network)
+ Faster internet connection than wireless network
- Needs a lot of cable, which makes it somewhat more expensive.
- Harder to connect on a big network, need to have a systematical wiring system
For wireless connection:
+ Highly efficient. No need for a wiring system.
+ Ability to choose many security systems to use.
+ Home-network friendly.
- Somewhat expensive.
- Wireless security systems are generally easy to break and hackable.
- Possible internet connection slowdown depending on the signal received.