All dynamics play a part in what type of barrel to get. Tightness of the bore, barrel length, quality, aggressiveness of the hop-up, and BB weight and quality. Different guns seem to have different results with different barrels, and different schools of thought suggest shorter or longer, tighter or wider is better. In the VSR family, which I believe the Bar-10 is, your using a VSR cut barrel. Consider getting a firefly hop-up bucking for starters, soft or hard depending in what FPS and BB weight you'll be using. I'd recommend staying with the stock length of inner barrel, but getting 6.03 tight-bore. Any tighter and your BBs may become unstable, but best results in the CSR family seem to be with the 6.03. Here's where I disagree with above; grab a Laylax (Prometheus) barrel, and not a PDI. Although PDI makes a good upgrade part, their barrels are nothing special. Prometheus makes a solid stainless steel, fluted inner barrel that has really set the standard.
If you're upgrading the Bar-10, you'll likely need to up your spring power to increase FPS. This will translate into you needing a better cylinder set, and a better engineered trigger assembly, which can end up being costly. Consider some barrel stabilizers as well.
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