Quick chargers basically charge your batteries at higher current, slow chargers are the opposite. Main disadvantage of quick charging that i can think of is the heat generated during charging process, this could degrade the chemical properties of the battery. However, this is all dependent on your charger's charging profile, good chargers are embedded with multi-step charging profiles to ensure a healthy charging process.
The way your fast/slow chargers determine if your batteries are fully charged are the same. When charging begins, the voltage of the NiMH/NiCd batteries climbs. At a point of time near to full charge, the batteries will approach a peak in the voltage reading and start to dip slowly to a steady value indicating a full charge. That is when your charger switches to a "trickle charge" mode (maintaining the charge in battery with minimal charging current).
If the charger is designed for use with NiMH batteries, I would say you're pretty safe to use it with the Eneloop batteries. But again, try at your own risk, there might be exceptions though since not all chargers are designed the same.