Mouser's warehouse is in Texas so that's a lot further from you. They're a lot closer for me. Newark does have good prices on stuff, but I don't use them all that often. If you're that close to them, maybe you could do a will call at their warehouse. That would be handy.
I've used Newark before, but not often so I don't recall the shipping options. I assumed they provided a first class mail option so the $10 shipping is rough, need a big order to make that worthwhile. Mouser lists an economy method for $5, but it's slow. For small orders at Mouser, I always ask them to send it first class in the shipping instructions and they always do it when I ask them to. For the bigger orders, I just use the Priorty Mail option for $7 since first class is only cheap when it's just a few ounces. Either way it only takes a couple three days.
For caps and resistors, I almost always buy them in groups of 100. They're so cheap and with the price break, there's no reason to buy any less than that. Though, some passives can get expensive. The high value MLCC caps aren't cheap so I usually buy them in smaller quantity. The inductors I use are like a dollar a pop so I'm not going to buy any more of those than I actually need. Current sense resistors are rather expensive as well.
For the MLCC caps, the price goes up a lot for values above 1uF. Anything below that I can usually get at Mouser for under a buck with a quantity of 100. So, I would expect the 4.7uF ones to be where you see a big price difference.
The 22uF MLCC caps I use are like 50 cents a piece at Mouser for quantities between 10 and 100. I looked and the pricing is almost the same at Newark. I've seen pretty big variations in price at Mouser for parts that are very similar. You really have to scrutinize the parts listings and seek out the less expensive ones. I've found it's mainly the ICs where Newark does a lot better than Mouser. If you want to get really hammered on stuff, head over to DigiKey.