Xerotolerant's answer basically says it all already.
pickups are better to use with acoustic instruments than a microphone?
No, pickups are in principle almost always worse than microphones, as far as sound is concerned. They sound alternatively tinny, boomy, scratchy, clickey or undynamically-boring, depending on the instrument and particular pickup model (there are very different ones). For recording purposes, I would always try to catch every acoustic instrument with at least one microphone, with the exception of acoustic instruments that aren't really used acoustically (e.g. wah-wah violin, reverb-drowned percussion guitar, synth-bass–triggering trombone or distorted cello).
However, when you need to make an instrument loud for a live gig, you usually need to make a few compromises to ensure everyone actually hears it properly. Microphones have a whole bunch of problems:
- Decent condenser mics are very sensitive to vibrations / touch. In the typical hurry of a live sound check & show, you're in for a lot of noise.
- All of them don't like to be dropped, and the best ones are really expensive.
- Quite heavy, too – a large-diaphragm condenser sounds gorgeous for many instruments, but it's really unwiedly.
- They need to be placed carefully. The ideal position sometimes means you have an awkward mic stand in a stupid position on stage and the performer must not move more than a couple of inches in any direction.
- Signal bleed. Any mic on stage will pick up all noise that's coming in. For brass, drums and guitar amps this is scarcely a problem because the signal you want is so loud that you can turn the gain way down on the console (thus making bleed very quiet). But most other instruments are barely loud enough to be heard at all; sometimes a mic close to the instrument will pick up more sound from the drumset on the other side of the stage! This makes it very difficult to dial in a good mix that actually brings out these instruments.
- Feedback is of course down to the same problem: the PA and monitors also bleed into the mics, and if the mic itself is audible on those speakers then you have a catastrophic loop.
Most of these problems can be at least mitigated with small gooseneck microphones mounted right on the instrument (or even in the instrument), however it's seldom possible to place these mics in a way that would give the best sound. Close-miking string instruments gives to a lesser degree the same scratchy character that most pickups are notorious for.
Thus, for most live applications, I much prefer at least having a pickup for string instruments. In particular, I very strongly avoid putting any mic signal on monitors.
Then again, some pickups also don't give any benefit over even a cheap-ish gooseneck microphone. In particular, there are contact mics that can be sticked on most any acoustic string instrument, but in my experience they tend to give a much more boomy, indirect sound than a mic and are almost as feedback-sensitive.
I thus prefer pickups that more or less directly pick up the string vibrations – piëzo bridge pickups for bowed strings and classical guitar, and magnetic pickups for steelstring guitar. Those can be turned on relatively loud even on monitor speakers. These pickups generally sound quite harsh, but with careful EQ and reverb you can usually get result that's satisfying for live. But that requires a fixed setup for each instrument individually.
If you have so many mics and can't afford installing a high-quality pickup in each, you'll thus fare better with a single mic. If you don't play with other very loud instruments, I suggest a small-diaphragm condenser like Oktava Mk012 or AKG C1000, which you may have to move a bit on its stand. If you are playing with loud other instruments, use two Shure SM57 instead, one for guitar and ukulele (very close over the fretboard and pointing at the sound hole) and one for the violin and viola (alternatively a gooseneck clip-on that you can switch between the instruments).
If you use mics and need to hear your instruments on stage (in fact, even if you use pickups), in-ear monitoring is much better than floor monitors.