I don't know of any days with Vigils (causing one to fast & abstain) that aren't also "big enough" 1st Class feast days which override Friday abstinence.
In other words, fasting on both days would be almost as bad as fasting on neither. You're not supposed to mourn when the Church rejoices. Are you really of the spirit of the Church when you do this? We should *humbly* follow our Holy Mother Church and Her liturgy.
I think the most perfect would be to fast/abstain on Thursday and enjoy meat on Friday.
And yes, there's a time to eat meat and celebrate -- feast -- on major Feast days. What would the saints do? They celebrated the Church's great feast days.
But any time a Feast overrides a Friday abstinence, you don't have to worry about missing out, because the Vigil has you covered there. You get your penance in, just a day earlier.
P.S. This only applies to the United States and any other countries where the Immaculate Conception has the same status.