There are 3 considerations in choosing lamps for plants, vs. lighting for the human eye: PAR, PPFD, and the duration of both. Let me explain. PAR (photosynthetically active radiation) are the violet, blue, and red wavelengths needed by the "higher" plants that most of us grow. These wavelengths appear dim our eyes even at high wattage or lumens, so "bright" lamps are an eye thing irrelevant to plants. The amount of the colours/wavelengths ROYGBIV in a lamps is revealed by its "spectral power distribution" graph (SPD). The company who makes the lamps will often fax the SPD graph to you if you cannot find it on the Internet. I've got piles of them. By keying in on your browser, "spectral power distribution of sylvania fluorescent lamps" you can see examples of what I'm talking about.
Then I compare these lamp graphs to the "absorption spectra" of plant pigments, namely chlorophyll a, chlorophyll b, and the carotenoids - particularly beta-carotene. Plant pigments will either reflect off the wavelengths that your lamps provide or will absorb them for photosynthesis. They reflect off most of the green, yellow-green, yellow, and yellow-orange wavelengths that just so happen to appear as bright to human eyes. Absorption spectra graphs reveal that violet, blue, and red (PAR) are what are needed for photosynthesis, and CRI of lamps don't indicate what colour wavelengths are in a specific tube. "Cool white" and "warm whiate" terminology is equally useless! Light intensity in watts or lumens do not refer to how much PAR is available to a plant, and is also irrelevant to how much PPFD (explained next) exists.
The measurement of how many usable photosynthetic wavelengths actually reaching the leaves (its density) is called PPFD, or photosynthetic photon flux density. This is about usable photons. And if the PPFD is not enough in your lamps when the PAR is relatively good, many plants can make up their need for a daily amount of carbohydrate production just by settin the light timer to remain on another 2-3 hours.