They handle fairly well for heavy FWDers (they have the transverse fiberglass leaf springs) and in 3.4DOHC guise, they can keep up with the V8 Mustang of their day.
They do have their issues though. The alternators are undersized and in a terrible location on the bottom of the engine. So in addition to being overworked, the alternators have heat dissipation issues which just kills them all the faster. It was bad enough that GM saw fit to engineer a cooling duct that ran from just in front of the radiator back to the alternator. Step 1 of alternator replacement is "Remove front right wheel assembly." Not good. Once it was time for my second replacement, I spent the extra money and took it to a GM Goodwrentch dealer to get the lifetime warranty.
The timing belt is probably the most notorious thing on these cars. Since GM just took an existing CIB V6 and slapped a DOHC valvetrain on it you can imagine the resulting mess. First, in the earlier years of this engine, the tension pulleys for the belt were made of plastic and just plain didn't hold up. By '94 they were metal but the assembly they were attached to was plastic. GM didn't see fit to put timing markers on any of the gears. If you lose the belt without timing marks, you're sunk. You have to open up the engine and manually set the timing. The icing on the cake was that even if you were vigilant and wanted to change your timing belt at the proper service interval, it was virtually impossible to do in your home garage... or even a local mechanic. It requires a special tool to hold the timing sprockets in place and even then the engine is so tightly wedged in there you need to put it on a lift to access the bottom side. Interesting trivia fact: This engine technically has 5 camshafts. GM had to leave the original camshaft in the block because the oil pump was powered by it.... at the opposite side of the engine. It has no cam lobes however.
The brakes are severly undersized and though they stop the car ok, they burn up in about 15k miles. I was so used to changing brakes every 15k on the Cutlass that I started getting worried when I was at 30k on the CTS. I took it to Meineki for a free check and they said the pads were a 10 out of 11.
There is a minor issue with the transmission that you only find if you are driving VERY hard. If you take a hard left hand turn at speed all of the transmission fluid will slosh to the right, starve the transmission, and it will drop out of gear. Once the fluid sloshes back the transmission picks back up again and slams back into gear. This only happened to me twice. There are actually instructions out there for more hardcore W-Body drivers on how to add baffles to the bottom of your transmission pan to prevent this from happening.
Changing the spark plugs is a chore. You have to remove the electric fans, remove the upper motor mount, put the car in gear and have your buddies push the car carefully until the motor rotates forward. This is the only way to access the rear plugs.
Now for the good:
As I mentioned, the car handles great for a relatively heavy FWDer. There is a lot of aftermarket support for tightening up the body roll... the car's only big handling offense. Mainly better bushings and thicker roll bars. You can also get stronger upper engine mounts if you're really hardcore.
This is the only convertible post 1985 that you can comfortably put yourself, 3 friends, and a week's worth of luggage in with the top down. And I mean comfortable. The rear bucket seats are supportive in every way. There is plenty of legroom all around and the ride is soft without being floaty. My CTS's seats were comfortable but the Cutlass easily eclipsed that. With the top up it was just a Cutlass Coupe. There was zero intrusion into the trunk from the convertible mechanism with the top up.
Even with all of the issues the 3.4 Twincam has, I'd still never buy a Cutlass without one in it. It revs high and fast and doesn't seem to have that weak spot that some DOHC engines (cough honda cough) at the low end. There is no V-Tech to kicketh in yo. It's just up up up till you hit the rev limiter. It will chirp second if you're not minding your right foot. The only way you ever got the advertised 29mpg highway was on a downhill straight road at 55mph. I never did better than 28mpg even when I was trying hard.
The convertible was great. I'm not sure if the roll bar helped with this, but with the windows up I could cruise around with very little wind interference. The result was a rather crazy looking guy cruising around Pittsburgh with the top down wearing a leather jacket and gloves in 49 degree weather. I'd just put the heat up to max and I was fine. The adverts from Oldsmobile stated "From zero to wide open in 12 seconds" Putting the top down became as routine as putting down the windows.
As long as you know what you're getting into, and have a AAA membership, these cars can be a real treat (honestly) to own. I'd love to re-add on to my currently non-existant collection some day.