Very dificult to answer this question without asking questions ,what type of fence do you have ? how high is it ? do your fence posts extend above the top of the fence ? if fence panals how long are they ?

Might be cheaper, but doesn't look as good, and is quite fiddly to do. Plus the mesh, if you grow anything up it, has a tendency to collapse in the middle with the weight of a plant, unless you have a batten along the top to which it is attached.

I wonder if it would be any cheaper than trellis if you make your own trellis out of roof battens. Sometimes you can even get hold of old battens removed from an old building being re-roofed if you know any roofers.
I might be a cheapskate, but home-made trellis lasts just as long and is usually stronger than the stapled together tat which most garden centres sell.