You can get the best of both worlds by going modular. Do your first 180 hours anywhere you like - PPL, Night, SEIR and MEP. Then, if you must, go somewhere 'Big' for the last 20 hours MEIR and CPL.
Your CV will read "CPL & MEIR training completed at (Big name) flight training."
Keep it simple. If they ask integrated or modular, or where you did your PPL then tell them, but don't offer them anything more than they ask for.