We have used both, drilled piers and driven piling, on two units at the same site (units were designed & constructed 10 years apart).
Drilled piers can be constructed in larger sizes and each one can do the work of several driven piling. This often gives drilled piers a cost advantage over driven piling.
A tuned turbine-generator pedestal, to control vibration, can be designed using either drilled piers or driven piling.
That is where a detailed geotechnical program comes in. The results of soil borings, field & lab tests, pile / drilled pier load tests, etc. are essential. For large units, I suggest allowing 2 or 3 months (or more) to collect and analyze the geotech data before making a decision.
I am not a big fan of concrete spin piles. The method was developed as a very economical way to make concrete pipe. Someomne then got the bright idea to use it as a foundation element. The problem is that there is a lot of variability in the thickness and concrete strength. If you are concerned about lateral load, I would consider other pile types.
All pile types have their pluses and minuses. Certianly a drilled shaft will accept lateral load, but so will many pile types.
The best pile choice depends on many factors
Site conditions:
overhead clearance
accesibility
neighbors &work hours
underground utilities
Geotechnical:
Soil type
Soil strength
Obstructions
Depth to rock
Liquifaction potential
Other Considerations
Design life
static or Dynamic loads
This is not a complete list, but does show that one can not make a statement that foundation element X is better than type Y. A whole host of project specific factors should be considered before chosing a pile type