Like Dave Tittle - A good friend - I am in Dallas, too.
I have a '93 RT/10 and '98 GTS and I have a C4, so at least I have some personal experience.
If you expect to daily drive the car, you will have to be willing to sacrifice tons of creature comforts to go from a C5 to a '92-'96 RT/10. These GEN I cars have no outside door handles, no roll-up windows and the hardtops cannot be stowed in the trunk ('96 RT/10 is sort of a hybrid but suffers from these same problems). So, to be frank, the GEN I RT/10 is more of a fair weather toy than a daily driver (although many folks do daily drive them). That said, I LOVE my RT/10 and in many ways prefer it to the more "refined" GTS.
As for the driving experience, I have to say that you will notice a HUGE difference in the RT/10 over a C5 in terms of raw power. But the Viper will bite much more easily; no ABS, no traction control, no other driver aids.
With these caveats, there is no question that I prefer the Viper to any C5, stock for stock. Tittle has an awesome Z06 that is essentially as fast on a track as my RT/10 or perhaps faster, but I prefer the primal experience of the RT/10. With a skilled driver, I think the RT/10 is faster overall.
Then, when it comes to modifications, I have to say that I prefer the Corvette. If you are a DIY person, there are precious few options with Vipers, and my C4 is my "fast" car (at least in a straight line). The volume of C4 and C5 cars make aftermarket parts less expensive and more available, especially in the engine department. While I can personally perfomance program the PCM on my C4, I cannot do so on the Viper and do not see any real hope on the horizon that an end user will have the ability to reprogram Viper PCMs. Notice how Tittle is looking for a C5 as a project car and not a Viper; he's a DIY guy, too and I suspect his preference hinges on similar concerns.
At the end of the day, for a daily driven car, I would strongly consider a used GTS. If you plan to leave it stock, the Viper just blows away any Corvette ever made in looks and performance and the Viper holds its value very, very well. I figure my '93 RT/10 is worth at least $35K (lower mileage examples are worth more), not bad for a car that cost about $52K when I bought it 7 years ago.
If you want to know or see more, I highly recommend vising with Dave, and I will be happy to show you my RT/10. Dave's GTS is awesome, too, and a great choice if you are willing to step up to a GEN II car.
Keith