When is it worth competing to farm fields?
If you're losing because your opponent is scoring fields and you aren't, then yes, you will have to fight for those fields.  The tricky thing with fields is that you have to commit to them before you know what they will be worth, so try to estimate in your own mind what a field will be worth at the end of the game and factor it in your calculations.

Watch out for the "cloister with a road" tile coming out early, this will cause there to be one large field at the end and a big fight for the farming.

If fighting for the farming doesn't suit your playing style then try to play in a way that prevents large fields forming -- use road junctions to break them up and try to stop people creating loops with roads.  Then build your cities away from the big fields.  Additionally, opponents who commit heavily to farming early on will be short of meeples during the game and you should be able to bully them during the game by playing tiles to slow or prevent them from completing their cities/roads/cloisters, or joining your meeples into their cities generally obstructing their completion.  With your spare meeples you should be able complete lots of features and rack up the points.