In My opinion I would place the stand in the hardwood river bottoms if you are looking for that big buck thats most likely were he will be either chasing a doe or just in the cover. Although if you waant a better chance of getting a deer i would have to go with the feild you have a better chance of seeing a variety of deer.

What kind of sign are you seeing at each place? Remember that deer love edges, so the field corner might be fine, or at the edge of the river bottom hardwoods rather than in the middle of them since it can be real open in hardwood stands. Which ever one you choose, I hope you get a big 'un.

riverbottom

My first choice would be the river bottom, but I'd have a stand in both.

The biggest buck would most likely be found in the riverbottom, they don't get big standing in a cut corn field during gun season. Look for gully edge in the riverbottoms, this could be just a hill up so hang a stand on the top of the hill,they love walking on the top of the gully.

You will probably see more deer in the field, but you might see a better deer or get a closer shot in the bottom. I am a woods hunter myself and I don't like to hunt fields that much, but to each his or her own.

You got a better chance of seeing more deer in the field. But the big bucks are in the river bottom.

I would hunt both. Hunt the river bottom in the early morning or late afternoon and during mid day I would hunt the field. The deer (both small and large) like the open fields for both food and social interaction. The big bucks will travel from the river bottoms to the fields sometime during the day (in my experiences in the past). Good hunting.