The search engine is much better. You can do google-like searches, just type what you're looking for, and select the best match from the results list. In Osmand and all other open source apps, you have to first type the country and region where you think your target is located.

Also, it's very easy to start downloading an offline map for any region - just zoom in on a new area, and it provides the link for that region. Right now it's free, unlimited and it works all over the world (though of course that can change in the future). I haven't figured out how to do the same thing in Osmand, and it says the free version is limited to 10 maps.