There are tons of variations on this situation; a lot of it will depend on your cameras (both film and digital), as well as what you typically do with your photos. If you only tend to upload to Flickr it's a very different answer than if you like to print at 20x30.
Anyway, I'd say the basic situation is this:
A simple print from a color negative will look a lot like a simple print from straight-from-camera JPEG. And I mean a lot like it; they're being printed on the same machines, with the same color correction, and so forth. From Target, etc, they'll probably turn out a little over-saturated and gaudy, but 40 years of colour photography has shown that's what most people like.
For anything more complicated, you need a good custom lab, access to a darkroom, or – having ruled those two out – the current favorite of mainstream film users: scans!
This is where digital's advantage really picks up compared to the chain stores: you don't have to scan it, you've got the full-quality image right there. Getting good scans from chain stores is quite hit-and-miss, large scans suitable for large prints might be too expensive, or not even available. I'll emphasize that it's definitely worth checking out all the options locally; it can vary even between different stores in the same chain.
That said, I think the "typical" situation would be that the simplest chain-store scans are usually the size they'd use for their normal size of prints: suitable for 4x6 or 5x7, perhaps 8x10 with a bit of care. For large prints, digital has a definite advantage.
For posting online, I'd probably still lean towards digital, but the quality you get from the chain-store scans is much more likely to be an acceptable level for Flickr or other online galleries - I think it's worth noting that some of the better film photographers I know on Flickr have found ways to work with chain stores only.
The scanning situation is why a lot of regular film shooters get themselves a scanner; you get better scans and better prints, and pays for itself pretty rapidly.
PS: I know it's not what you asked, and certainly not worth getting into for a few rolls of experimenting, but processing your own film is almost certainly much simpler than you think. If you find you like shooting film, it's definitely worth looking into a little closer.