The Oregon 450 series is lighter, and has a higher-resolution screen than the 62 series.
On the other hand, I did extensive comparisons in a shop (they let me borrow both for half an hour), and for my style of use, I found the 62 series to be much better.
On the 62 series, changing page (from map to trip stats to altitude profile) is a matter of a quick button push that can be done also with gloves. On the Oregon, you need several precise pokes on the screen; much slower. On the 62 series, marking where you are is a simple button-press; again, this is much slower on the Oregon. The 62 also has a somewhat more readable screen.
When I hike / ski, I don't wish to spend too much time navigating GPS menus. I wanted a device that was as fast as possible to use, for marking locations, storing trails, and getting a fix. I wanted to be able to pull it out, press a couple of buttons to mark the location, put it back in, and carry on skiing/hiking. I had the impression that I would find it slow to use a 450 in the field. The map in the 62 series is sufficient for my purposes (and if I need a good map, I use a paper map, or I can always wake up my Android phone, which has WAY more pixels and better screen than either, albeit shorter battery life). I also plan to carry the GPS in an outside backpack pocket, and the fact that the antenna of the 62s is optimized for vertical orientation is a plus, as that will be the orientation in which the GPS will travel.
The use of the original poster seems similar to mine, so if the price difference is not an issue, the 62 series may be more suitable.