You have several issues. One at at time.....
1. There is no such thing as an "HDTV" or "digital" TV antenna. Any antenna advertised that way is advertising hype to get you to buy it. A TV antenna is a TV antenna, period. A 30-year old antenna in good condition with a good downlead will work as good or better (probably better) than almost any modern indoor antenna you can buy.
2. A "good" indoor antenna? That depends on where you are relative to the TV transmitters. Any indoor antenna can be good if you're close enough to the transmitters. But for the vast majority of viewers, getting a "good" indoor antenna for digital television (DTV) in the U.S. is a major challenge. Many are finding that no indoor antenna will cut it--they need to put something up outside, even if an indoor antenna was okay with analog.
3. A "good cheap one?" That's probably a conflict in terms. Again, any cheap antenna could work, depending on where you are. By the same token, the most expensive one on the market could give you crummy performance on all channels. To help you decide which to expect, see the 2 links below for info on the TV transmitters in your area and what type of antenna you'll need to receive them.
4. This isn't in your question, but you need to know: don't count on the familiar "brand" channel numbers as being the actual channel freqency that any station is transmitting. Many if not most U.S. DTV stations are now transmitting on new channel frequencies; they've just kept their familiar "brand" number so that the public won't be overly confused. For example, my local channel "3" is actually transmitting on channel 35.
Why is that important? Because if I was buying an antenna to get channel "3," I'd actually want to be looking for a UHF antenna (to receive channel 35); the exact opposite of what you'd expect.
So check the links below closely, and you should come up with the right recommendation. Be prepared for the necessity of something that isn't "cheap" or even indoor.
Followup per your Additional Details: the eBay antenna does have telescoping rods, like any "rabbit ears" antenna, and those are for VHF. The other one has no visible VHF elements, so in that sense the eBay antenna is likely better on ch. 2-13 (VHF) than the Radio Shack model.
But really, instead of "better" you should consider it as being "less lousy." As a rule of thumb, there is *no* indoor antenna that relies on telescoping rods for VHF reception that will consistently give good performance on RF channels 2-13 (which in the U.S. means 7-13 with rare exceptions) unless the viewer is *really* close to the transmitting towers and there are no serious obstructions in the way.
Again, you should not be counting on decent performance from any indoor antenna unless the references I've cited indicated that an indoor antenna might work for you. If that's the case, there are two the merit consideration, the Winegard SS3000 for optimum UHF performance, and the Terk TV5 for the best you can probably do indoors on VHF. Try those in Google and see what you think. Either one should be far better than the two you're considering now.