I must say that I use modRana on PC and Poor Maps on the device so far. So, I haven't tested modRana too much on device. Assuming that you use the latest version of the server (there could be different problems with the versions earlier than 0.3) * you could be hitting timeouts for connections in modRana. As a result, modRana might ask multiple times for the same tiles. To check if its true, look into the events log shown in the server's main screen. Check whether the same URL is loaded multiple times.
* its probable that modRana and Poor Maps use different tile sizes. This is visible in URLs requested to render the tiles. Notice if there is a difference in "shift" and "scale" parameters in URL. Poor Maps uses by default 1024x1024 or 512x512 tiles that are not very well supported by modRana (or not at all yet) with modRana using 256x256 tiles (shift=0 and scale=1 by default). As a result, tile rendering can be done in bigger chunks in Poor Maps which should produce faster overall rendering. Optimization of tile size vs parallel rendering is not a simple problem and it may vary between the devices.
* maybe modRana's rendering is slower. If its true you could try to follow when the server states "Idle" on its cover and see when the map is rendered in reality. For that, browse the map in Poor Maps or modRana and peak by sliding from the right on the state of the server. In Poor Maps delay is minimal if any, in modRana - I haven't checked.
The main drawback of smaller maps is that you would have to change them in the server's settings.
Also, you cannot calculate the routes between maps.