You cannot really compare the two. Mammoth is one of the best mountains in North America. It has great steeps, consistent snow, a good park......
Big Bear is much smaller. It has a park, but Mt. Baldy has much better terrain if you are down south.
My wife and I go to Mammoth at least two weekends a month. We usually try to get a day in down south on the weekends we don't hit Mammoth. We usually go to Baldy if we are going to stay south, as it has much better terrain. That being said, if the people are not all that experienced Big Bear is easier than Baldy. It has better groomers, it is really more of a resort than Baldy.
Mammoth is about 6 hours from UCSB. I went to UCSB and was on the club ski team, so I was at Mammoth every other weekend. I don't know how far it would be to Big Bear, but it is not all THAT close to Santa Barbara, probably 3 hours. If you are going to stay overnight Mammoth is WAY better, but it is also more expensive, I'm assuming you guys don't have Ikon passes. If you do go to Mammoth, I would try to stay somewhere with good shuttle access to the hill and the village. You don't have to stay in the village, but you want to be able to take a bus to the slopes and the late night trolley back from partying. We rarely go out late when we are there, so I can't give too much advice, but the late night trolley is pretty cool. I would think lodging in Mammoth would be far more expensive than Big Bear, but I don't know details. We have a ski lease in Mammoth that we rent all winter, so I don't know what rates are like. I would imagine Valentine's Day weekend would be pricey.
Here is map with some of the shuttle lines. Parking can be a nuisance, so I would really recommend using the shuttle.
https://www.mammothmountain.com/transportation/free-mountain-shuttle
I absolutely love Mammoth, skiing wise you really can't compare it to bear/summit, but it is more expensive and farther away.
