There have been numerous discussions here in the past, which saw is best depends on the type of wood. A very soft and resinous wood requires a very open tooth structure, you either want a very coarse tpi or heavy gullets, optimally both. However a very fine grained hardwood needs the exact opposite as the soft wood saw will be too aggressive, catch, and be hard to pull through the wood without heavy force on the draw.
Felco makes a very nice soft sap wood saw, however it is too aggressive for small diameter limbs. Tashio Hardware makes very nice hand saws, their Timber saw is one of the general purpose saws I have seen for this area and works well over a very broard range of wood types from soft firs to harder oak and birch, going through trunks as well as limbs. They also have a very nice folding saw with replaceable blades with the ability to change the angle of the blade which is very useful.
-Cliff