I use a diffusor enlarger (durst ac800) that i aquired this autumn (my first enlarger). The few different types of enlargers I had access to before were also diffusor enlargers. The sharpest prints I've seen was however made on an old Leitz focomat 2c condensor enlarger. Luckily I found out that I can swap my diffusor lightboxes with condensor ones if I want to so I can benefit from both worlds on the same enlarger. I believe many diffusor enlargers have this ability and some condensor enlargers have room for a diffusor-filter.
I am no master printer (yet) but after what I've heard and read these are the main differences:
Condensor: Sharper, "salt and pepper" effect, higher contrast, some highlight details may disappear.
Diffusor: lower contrast (typically a grade less than condensor), dust is often blurred so it's hidden in the print.
The same contrast can be achieved by both but you will have to develop your film accordingly.
Tetenal lists development times for both condensor and diffusor enlargers in their Ultrafin manual.
Beta 0.55 for condensor enlargers
Beta 0.70 for diffusor enlargers
The times in the beta 0.55 column are a lot shorter than the ones for beta 0.70. Agitation also differs. Here is an example:
Ultrafin liquid 1+10 and Agfa APX 100:
beta 0.55: agitation every 3 sec, 4 minutes
beta 0.70: agitation every 1 min, 7 minutes