Generally, the larger the diameter log, the harder it is to press for most people. The larger diameter puts the weight more out in front, which takes it away from your centerline, which usually makes it harder.
Everyone is different though. Generally, the larger log is easier to clean for people than the smaller log.
Also--the length of the log makes a difference. A log that is exceptionally longer than standard makes for a harder clean and press for most people.
If you plan on competing, a 12" log would probably be your best bet due to the fact it is the most common size found in contests for men.
Don't forget too, every log is different. We have one 12" log that is heavy empty and closer to 13"-- very hard compared to our "standard" 12" log.
Different logs also help account for guys claiming to hit XXX pounds in training with their home log, but never hitting that number in a comp with different logs.
Sorry for rambling.
Cliff notes: 12" is harder. Get a 12" to train with.