Once you become accustomed to watching HD, analog signals will be at best, OK on an HD TV screen.
The resolution you are getting sent to the EyeTV is at best 720 x 480, compared to the monitor on your 24" iMac of 1920 x 1200. You will never stretch that incoming signal to anything acceptable in full screen on your iMac. However, anything you record should look fine when displayed on up to a 720p TV. Your recordings can and some stations will look as good as DVD (also 480) quality when displayed on a HD TV. Some lower tier stations broadcast junk video streams and they will typically never be acceptable except on a CRT, non-HD TV set.
Personally, would run, not walk, back to the store today and return the 250.... even if you haven't changed your TV's to HD yet and even if all the incoming signals you have available are in SD...
imho...Any salesman still pushing analog only tuners is doing a disservice to their customers, especially those who have already moved to HD, as the over-the-air analog signals are now scheduled to disappear at the beginning of '09. These tuners will basically become obsolete in about a year. Cannot recommend any tuner that does not have a digital tuner.
Don't be too mad at the salesman though. A lot of people still use and like that 250 non-Pro model. It was among the best out there for a Mac if you were wanting to capture analog signals. And it is totally acceptable on smaller monitors with resolutions of 800 x 600 and is OK even on screens up to about 1280 x 1024. Any higher resolution than that and it will be pretty bad.
Just keep in mind that your SD Sanyo is best case equivalent to 480 pixels. Your iMac has 1200. As xstep said, watching the incoming stream in a 480 window should give you every bit as good a picture as your TV. But, when trying to stretch it to full screen at 1200, as you've found out, not so good.
As far as ElGato devices with digital tuners, there are 3 options - the 250 Pro, the Hybrid and the HD Homerun. The 250 Pro and the Hybrid have both analog and digital tuners.