The short answer is: Done correctly, there should be no difference.
In reality, most beginners enjoy the (invariably false) sense of security of a Western saddle, given the “handle” (horn). At more advanced levels, this very much depends upon what you call “Western” and what you call “English”.
High school equitation (high school ‘dressage’) is essentially comprised of two rather distinct ‘schools’, ‘styles’, or ‘manners’ of training (dressage):
1. German School – influenced by its essentially Prussian cavalry heritage
2. Baucherist School – influenced by/consolidating an older and essentially Latin or Romanic heritage
The latter is often is often called “French Classical” dressage – though this rather obfuscates the matter, as both styles notionally pursue ideals emerging from a mostly French interpretation of European high school equitation canonized by François Robichon de La Guérinière (French), who preceded both schools.
You will find the more popular modern German flavor laborious as a novice (or as an expert, actually), given the heavier contact implied by the methodology and ideology – as heavy or heavier than other informally “English” sporting styles, e.g., cross country/show jumping, etc.
With the Baucherist style, the “handle” (feel of the reins/lightness) would be akint toa well trained Californio/Vaquero style/”reined” horse (of which there are approximately 3 remaining in the US 🙂 ) – one of essentially two types American “Western” style riding – and the one closest to its Spanish-colonial origins: Doma Vaquera (Spanish stock equitation – also an equitation of prevailing collection, i.e. the ‘artificial’ carriage implicit with high school dressage).
At a novice level, you are more or less “trail riding” regardless (whether upon a circle or in the woods), so: just pick the saddle style you like best for now and get to it!