Bruins (UCLA) Battalion vs. Surfriders (UCSB) Battalion? No contest, at least on which one has the cooler nickname.
Your post was a little unclear. It reads like you are applying to the crosstown affiliate of host UCSB. The GoArmy/Locate Schools does not indicate any affiliates for UCSB, though that site's reliability is not guaranteed (an Army website, who' da thunk it?).
Generally, the inconvenience of getting across town as well as the lower visibility and socialization opportunities are disadvantages which argue in favor of attending a host school. My son's dorm room was 30 seconds or so from the field where 6 a.m. PT occurred in contrast to the 15 or 20 minute shuttle van of his crosstown colleagues. When he was on the Ranger Challenge, practices began at 5 or 5:30, and there was no van. No cadets from the crosstown school did RC.
However, there are factors which could change the calculation. For example, UCLA is a huge campus, and many students are commuters. A few years ago there was a published report of a cadet whose commute via public transportation from his home in Brooklyn to his school, host St. John's University in Queens (i.e., the same city), took one hour and 40 minutes each way. Would you be living on campus or commuting? Is the cross town school three minutes or 30 minutes away?
By mentioning visibility, I am not talking about how many times you poke your head into the battalion offices. Rather, would your
location impede your ability to participate in battalion extracurricular activities or informal gatherings such as breakfast after morning PT.
As someone indicated above, there are large battalions with sizeable affiliates which offer their own PT and Military Science classes.
For the most part cadre doesn't care about which school cadets are attending. With some exceptions, cadre members don't stay at a school longer than three years before they are rotated into another job. Few of them have ties to the host school, which does not pay their salary. Many of the non-coms who serve in the battalion are not college grads and would have even less interest in school distinctions.
As suggested above, research would be worthwhile. Recruiting officers would be pleased to arrange for you to meet with cadets to get a flavor of cadet life. If there is a gold bar recruiter (a recently commissioned graduate who is helping until until his or her BOLC begins), that person could be a great source of info.