RE: which would be more of a trophy.
I think it all depends on what the circumstances are - how hard did you hunt, how much grief you got from the wife for those extra hours in the woods, whether or not you sat for a week, if you gave up a vacation day, etc. - it's not the method, but the hunt that counts.
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For what it's worth, a good firend of mine, and a retired professional wrestler (no, I know it's not real - but those guys are actually really physically fit) did actually wrestle a live deer and break it's neck (although the deer was wounded). Seriously, I saw the pictures ... the deer was down and out - a shot through the neck. It was dark by the time they found it, and they were very close to their vehicle (a brand new van), so rather than field dress it right there, they decided to take it back to camp to gut it. Halfway down the road, still high-fivin' each otehr, with a celebratory beer already under their belts, they had a strange feeling that something was watching them. When the driver saw the deer standing up in the van, he swerved, and when he did the deer lost his balance. Well my buddy instictively jumped out of his seat and onto the body of the now fully alert (and extremely scared) deer.
The deer was kicking and trying to get up (couldn't get footing on the slick floor of the van) - my buddy freaked and started yelling "SHOOT HIM" to the driver. Well the driver knew he couldn't just blast away with someone entwined in a p.o.'d deer .... so my friend had no choice but to hold on ... he eventually broke the buck's neck.
I know you'll be skeptical and probably think this is the b/s post of the year, but it's true.
I heard this the first time I ever met the guy, but when his 14 year old son ran into the house and brought out the pictures ... well, let's just say I couldn't doubt him any further.