@adil I know your reply is older but I feel like I understand it enough to give it an explanation myself.
Different between Local Path and AS Path prepend is:
Local Preference- is used to influence which pathway is used (internally) when there are multiple connections to the ISP. This option is not sent in the update to the eBGP neighbor.
-if you take another look at the example it shows the LP for Jack which is behind both edge iBGP routers. Router Jack will choose the Highest value Local Preference as the best pathway to reach the ISP. The ISP (eBGP router) does not see this preference.
The reason why you set the route-map for local pref inbound because you can influence the local preference value internally. This value is not included in the update to the eBGP peer.
Yes configuring LP on one of the iBGP routers should be enough as long as the local preference is set higher then the default of 0.
AS_Path Prepend- is also used when there are multiple connections to the ISP. It sets “fake” mutiple AS path hops on one router making it appear as if its much further then the other iBGP peer. From the ISP (eBGP) perspective it thinks the one with the higher hop count is further away so it sends traffic to the other iBGP router. All AS_Path prepend updates are sent to the ISP (eBGP router)
The reason why you set the route-map for as_path outbound because you are letting the eBGP neighbor about the prepended value