Hello Chris,
Both zones have quality hunting and will have mature bucks on public land. Zone 4 may have been hit a bit harder in the EHD outbreaks of '12 & '13 but age structures have recovered for the most part in both zones.
Zone 5 should have the edge on the amount of public land available but I haven't done an acreage comparison (never felt the need) so that may be an incorrect opinion.
You can do some homework from MO by accessing the Iowa DNR website and utilizing the Hunting Atlas and WMA maps to select areas that may be of interest to you before you come up this spring. Choose some areas that look good to you and then check them out this spring. The Iowa Sportsman's Atlas is also a very good resource.
Once you are up here, and if you find some public land areas that you really like, start knocking on some doors of nearby private landowners (a county plat book can be handy for tract sizes and landowner names) and you will likely get permission to bowhunt on some quality private land for FREE.
If you are only going to hunt for a couple of weeks, let the landowner know that so other hunters will have an opportunity to hunt during the season too (some landowners limit the number of people they give permission to).
The harder counties to get free hunting permission will likely be Taylor, Decatur, Wayne, and Monroe counties due to the amount of recreational land ownership ("deer properties" as opposed to "farm properties"), small outfitting operations, and higher levels of NR use (i.e., someone else has already asked).
However, I believe a courteous & persistent person could find free hunting access even in those counties. Spring is a great time to ask permission as fewer people are thinking about deer hunting. Asking permission to turkey hunt and getting some knowledge of the property is another way to develop a relationship, evaluate a property, and get an "in" for bowhunting in the fall.
Sorry for the long post, good luck to you this fall.
Take Care,
Tom