I have a Henry Big Boy X:
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It shoots .357 pretty good; .38 Spec not so much. I just shoot it with the irons - they're fiber optic, and I usually just shoot 50 - 100 yds. I don't know how it does at longer ranges. I believe Henry also makes a wood-stocked version.
My friend has a Henry Big Boy in .44 mag. I love that gun! It is a hoot to shoot and I love the receiver loading gate plus the removable tube magazine. It is on my list for "some day". I would imagine a .357 version would be as nice if not a nicer shooter than the .44 mag version. The Henry lever action should be a great match for .357 as far as accuracy. If you need more accuracy than a lever gun will give you then you need to also choose a more accurate cartridge than a .357 for serious bench rest work.