Both BCW and Ultra Pro sell 9-pocket, side-loading binder pages built from acid-free, non-PVC plastic. Side-loading matters more than the brand: it's the design that keeps a card from sliding out when the binder tips or gets picked up wrong, and both brands do it the same way.
Where BCW wins
Price. BCW is consistently the cheaper binder and page option at the same archival-safe spec, without paying for a license. If a binder's only job is keeping a collection organized and protected, BCW gets there for less.
Where Ultra Pro wins
Ultra Pro is the only one of the two that makes officially licensed Pokémon-branded binders, alongside Magic and other game lines. That license is the entire price difference; the archival pages inside perform the same job either way.
What neither does
Neither binder is a shipping container. A binder page holds a card for display and light handling, not the trip through the mail. If a card is going out for sale, it goes into a toploader and team bag before it leaves the binder.
Shop BCW on Amazon → (paid link) Shop Ultra Pro on Amazon → (paid link)