PCA9685 is the board that I am using for servo control by I2C. It's cheap, like $2.00 us from China. Can control up to 16 servos.
Hobby servos aren't as precise as stepper motors, or as repeatable. Stepper motors with some sort of gearing, like 10:1 geared are strong and very precise and repeatable when microstepped.
You don't have to spend a lot of money for them either. You can get a ramps 1.4 board for an Arduino along with some A4988 stepper drivers for around $30.00. They are good for steppers of approx. 1.5 amps. Not complicated to control either.
Nema 17 size steppers with a 10:1 gearbox are around $50 each. With microstepping you can easily control their movement to 1/10 of a degree. Way more precise than servos. Mine are set up for 89 microsteps per degree of movement.
Take a look at the fancier robot arms, and they all use stepper motors instead of servos. Some use geared steppers, others use belt drive or external gears to multiply their torque.
It all depends on how strong and accurate of a robot arm you want to build.
If your budget is thousands, you can build something really cool like the AR2 robot arm.
Here is what looks like a pretty good servo driven robot arm:
