I'm actually in the middle of this right now.
I have a '97 Riv S/C w/50K miles and am in the process of looking for an ETC. The Riv is my 2nd 3800 S/C (the first being a GP GTP). Both are/were great cars. The main differences between the Riv and the Eldo that will be a reliability issue are the N* headgasket issue, and the complexity of the road sensing suspension (RSS) in the ETC. I've read that the 3800 S/C's transmission is weaker than the N*'s, but I don't think that it's a major issue.
The 3800 has good power, especially right off the line -- but where the N* just gets going on the highway, the 3800 starts running out of steam. IMO it does not drive as well as the N* (which is the main reason I want the Eldo). And I hate the sound of the 3800 which sounds puny in comparison to the N*. Admittedly, I'm being pretty picky. The Riv drives very well on the highway. Both smooth and responsive. Obviously it's not a 5 series BMW, but it's not a Fleetwood either. The Riv is solid as a rock though.
I would say that the Riv's styling is more distinctive than the Eldo's. There is nothing else like it, for better or worse -- you either love it or hate it. The Eldo is much more conservative. The trunk is spacious, but oddly shaped. It's very narrow at the back end. It is deep, though. The Eldo's interior, IMO is much better. The Riv's is pretty stark, yet it's very distinctive. Again, you love it or hate it. I like the Riv's interior, but I just like the look of the Cadillac interior better.
The Riv does not have as many gizmos -- barely adequate stereo that is hard to upgrade due to the depth of the dash, no trip computer. TERRIBLE cupholder/cubbyhole areas for cell phone, etc. However, the CD storage area is easy to take out and makes a great place to install an XM radio. The Riv's front seats are comfortable, the driver's has both heat and lumbar (not sure if the pass seat had those as options), but I prefer the Eldorado's seats. It has actually very good rear seat room for a coupe -- better than the Eldorado. My Riv does not have a sunroof, but it has a TON of headroom.
I bought mine almost 2 years ago w/38K miles for $7K. I've put on new tires, a water pump, new brakes, new battery (which is vented, under the rear seat, and expensive...), a subwoofer in the trunk, and the XM Radio custom install. It has never left me stranded other than when I needed to jump it before getting the new battery. The only thing wrong w/mine is that the fuel gauge doesn't work accurately. I just use the trip odometer and get gas when I hit 200 miles.
I say all that to say that other than the reliability issue, the main benefit that the Riv has over the Eldo is the price. You should be able to find one for a few thousand cheaper than an Eldo w/the same year and mileage. I get about 15 MPG in town w/my Concours and I probably get 16-17 w/the Riv. On the hwy, I probably get 22-23 w/my Concours and 25 w/the Riv. The Riv does require premium fuel.
It's a great car, I'm just ready for a change. My parents are buying mine as a 2nd car. I wouldn't recommend it to them if it wasn't a good car. If you can find one, it makes a great daily driver.