I used carbonation drops in the bottles on my first batch and worked well. On the next batch, I measured dry sugar into each bottle. Lot of foaming. I haven't tasted it yet. What can I expect? Also, how do I mix sugar into the whole batch without stirring up the sediment on the bottom?
Carbonation drops are mostly sugar (and glucose), so as long as the amount is the same it should carbonate the same.
Beer out of the fermenter typically has about 1 volume of carbon dioxide dissolved in it, left over from fermentation. When you added the sugar-crystals, the thousands of nucleation points helped the gas be released quickly.
So there shouldn't be too much of an issue here. The sugar falling in may have pulled a little oxygen into the beverage, but in-bottle-fermentation should clean up most (if not all) of this. In future, add the sugar crystals before the beer (I assume beer, you don't say) in the bottle.
To "bulk prime" a full batch, a lot of people decant the beer into another vessel, typically something like a "bottling bucket", leaving the yeast behind. Enough sugar/honey/DME is dissolved into this for the whole batch at once.
I have used both.
The drops make it easy and simple but can get expensive. I used them for a hard cider so I knew exactly how much each bottle was getting so to not over-carbonate. It helped make sure each bottle was evenly primed.
For normal ale and lager I prefer to mix 5oz of Priming Sugar (corn dextrose) with 1 cup water and add that mixture to my bottling bucket. Mix it together with your wort then bottle.
Both work. It really comes down to what works best for your budget and bottling process. Try both for yourself and compare the results.