"Would you like to come over?"
This wording is a little less direct and gives the listener more of a choice. In most contexts they can answer either "yes" or "no" without feeling too much pressure either way. By wording the question this way you are genuinely giving the listener a choice.
"Will you come over?"
This wording is more direct. The listener still has the choice to say no, but in most contexts the speaker is seeking a "yes" response.
In either case, tone can make a difference (as nanren888 has already indicated). Either wording could be used for a friend. If you want to give them the option to come to your house, use the first (Would you like to come over?). If it is really important that they come over, use the second (Will you come over?), maybe adding "please" at the end as a courtesy.
In fact, "Will you come over?" would actually be used more with friends and family than with strangers. It might be considered rude or strange to be so direct with someone you don't know very well. But with a friend you can be more direct since you know they would only say "no" if they absolutely could not come (and they know you would only be so direct if it was something important).
I hope that helps!