Hello Aspirant, 

Both type of colleges are good for BA LLB integrated course and there is nothing going for or opposing the odds by getting any affiliation. 

UGC affiliation is provided to the universities surpassing some educational standards while BCI( Bar Council of India) affiliates only those colleges which have some quality standards in the field of law education and the whole panel consists of Lawyers from all over the country.

So if you get a college with BCI affiliation and a UGC affiliated university with no recognition for law education, you should go for the college with BCI affiliation as it is really going to help you..