A reciprocating saw, even with pruning blade is a bit of a pain, the blade doesn't move far enough to clear the saw dust if the branch is very thick. A hand saw like
these are VERY effective, and professionals will use them in preference to a chainsaw in many instances.
Electric chainsaws are relatively cheap, and Alko, Ryobi, Makita are reasonable makes. The problem is, it doesn't stop there. The cutters need frequent sharpening, so you need files, bar vice or chainvice, chain oil, gloves, trousers, helmet, and the list goes on. If you are cutting near the ground (felling?) the cutters have to go through bark which has grit particles splashed onto it by the rain.
I have a very large hedge, and a long handled pruning saw, and a Silky are easier to maintain it than a chainsaw IMO.
Axes can pull your shoulder or elbow unless you are young and fit.
Where are the trees situated, and how big are they? Leylandii are a difficult tree to deal with, and if you have to get off the ground, it is a whole different ball game. Trees weigh a lot, and can do surprising things on the way down.
Can you post a picture?