The RCC conversion is universally accepted throughout the Jewish world, including Israel. Nobody will question your Jewish bonafides once you achieve it. The Los Angeles Beit Din is an easier route even though they reject nine out of ten applicants.
The RCC track will take you at least two years and will usually demand weekly tutoring and obstacles. They’ll put the fear of God into you so that if you’re a woman, you’ll never want to be caught in public wearing pants, even when out for a jog.
Converting through the Los Angeles Beit Din will typically take about a year and will require weekly classes, knowledge of Hebrew, Jewish history, Jewish law and plenty of memorization of key blessings.
The RCC will always be looking for an excuse to kick you out of its conversion program. The Los Angeles Beit Din will give you a fair chance. Neither are going to come to your house and check that everything is kosher. Both will rely on the vote of confidence of your sponsoring rabbi.