competing companies vs companies that compete
“companies that compete one day” – one day refers to the verb “compete” -> logical.
“competing companies one day” – note that “competing” is an adjective. “one day” seems to modify “companies” – Illogical.
this basically states (remove the modifier) – “Companies one day may be partners the next” (they are companies on one day; later they no longer are companies but are partners).