The other Mark S did a good job describing the differences, and viva la difference!
The Upside of the Catskills:
The trails and camp sites are less crowded.
The bears are not aggressive (except near settled areas and large campgrounds).
There are more open woods to bushwhack through.
The terrain is easier to read and it is harder to get lost (IMHO).
The numbers of biting bugs are less than the other northeast mountains.
Mud season is generally not as bad because of thin, sandy soils.
The forests are predominately hardwoods which is nice in the autumn, although with less reds than the northern mountains.
The horizontal Catskill rock strata explains why there are so few slides. The soil cannot slide off as easily as it does on the slanted bedrock of the Adirondacks. The few Catskill slides are loose rock slides on very steep slopes. These can be more painful to climb compared to those smooth slanted sidewalks in the Adirondacks. The Friday Mt slide is probably the most fun with nice views. The older Slide Mt slide is now overgrown, and reportedly a painful walk on loose rock.
There are many fine views, often not right at the summits, e.g. Buck Ridge on Westkill, the two meadows on Ashokan High Point and its lower summit, the cliffs on Overlook, Huckleberry Point, Dibble's Quarry (with rock furniture) on Sugarloaf, Palenville Overlook (more rock furniture), Indian Head (aka Profile Rock), Poet's Ledge, the many viewpoints on the Escarpment Trail around North and South Mts. The views can be hazy, and its usually a view of more rounded green mountains rather than craggy peaks.
Because the Catskills have been more settled than the Adirondacks there are lots of interesting place names, e.g. Elfin Pass, Goblin Gap, Devil's Pulpit, Devil's Kitchen, Hell Hole, Alligator Rock, Sphinx Rock, Cod Fish Point, Fawn's Leap, Naiad's Bath, Niobe Falls, Rumble Tumble Falls, Peekamoose, Bangle Hill, Giggle Hollow, Barkaboom, Bullet Hole (two of them), Cradle Rock Ridge.
The Catskills are just plain fun to hike.