Handsaws.

There's nothing quite like being able to climb out an entire crown with just a handsaw. Pulling up a chainsaw can be annoying, although it is sometimes necessary. In each instance, I find that different handsaw placements can be beneficial to certain situations.
Typically my first and favorite placement is the leg mounted saw, with leg straps or the popular sawpod mounting system. I find that when I'm working large crown cleanings and the specs are to remove deadwood of a smaller diameter, I know that some work positions will be challenging, and usually of a horizontal nature at the ends of branches. Because of this, I don't like to be poking around for a dangling scabboard that's attached to my saddle while my core is burning to be released. I can give myself the advantage by moving my leg to a position that easily allows me to access my saw while fighting a not so favorable position.
On the other hand, when an operation calls for a longer duration of spar work and standing on gaffs, a scaboard that's mounted on the saddle may be the ticket. Climbing in an upright position doesn't favor bending over to grab a saw that's mounted on the leg, although some climbers out there may digress. Also, a leg mounted scaboard over gaffs can cause some unnecessary bulk, which is my biggest turnoff. Plus, during a removal situation that requires blocking out big wood, a handsaw won't do much good except for cleaning some small suckers out of the way or finishing a few fibers of a cut.
For me it's a question of mobility and economy. When I see tougher working positions and a lot of movement through the crown, the leg-mounted saw is my favorite option. A situation like a conifer removal or some type of other heavy spar work causes me to switch my saw placement over to the saddle.
I've even seen a fixed scabboard on the climbing saddle. This seems to converge the concept behind each postion. Rather than the saw dangling from the saddle, it remains fixed in place so that returning the saw is the same always.
I know there will be the argument out there by many arborists that they are creatures of habit, and that they benefit from having the same saw placement all the time. For me, it's as easy as having two hand saws set up for each situation. I keep a section in my utility body reserved for all things pruning, and two pruning saws of each nature really doesn't eat up that much space.
It's really a matter of convienance, as well as considering the task at hand. Personally, I like options.