As the ingredient list goes, both have a pretty simple one, without comedogenic or irritating ingredients, which is a big selling point to me. They are both targeted to people with sensitive or dry skin, so it should fit most, but from my experience, the L'Oreal Sublime Soft Pure Micellar Cleansing Water seemed to dry my skin in time.
While the L'Oreal version seems to dry my skin, Bioderma Sensibio Micelle Solution seems to irritate my eyes a bit. It doesn't sting or anything, buy my eyes are so red after using this to remove my eye makeup. I find that both, Bioderma and L'Oreal, don't excel at removing waterproof mascara or eyeliner and you need to do a little bit of rubbing in order to remove everything.
Concerning the "power of cleaning" face makeup, Bioderma definitely stands out! When using the Bioderma Sensibio Micelle Solution, I remove all my makeup with 2 big cotton pads, while using the L'Oreal one I need around 4 big cotton pads to be sure my face is clean.
Price wise, a 500 ml of Bioderma Sensibio Micelle Solution (which is one the one I usually get, though in the picture is a small 100ml one) costs around 17-18€, while a 250ml of L'Oreal Sublime Soft Pure Micellar Cleansing Water costs around 5€.
Which one I recommend?
I totally choose Bioderma for myself. I use it for almost 1 year and it haven't failed yet. Though I need to have a separate eye makeup remover, that's fine with me. I don't say the L'Oreal product is a bad one, but it's just not for my skin. Also, because it runs out faster, money wise, I think it's the same. If you want to give a try to micelle solutions, you can try the L'Oreal one, to see if they are for you, before stepping up and buying the Bioderma. Also, keep in mind that cosmetic products, usually work different on different people.
Which one do you prefer? What are you using to remove your makeup?