(Rick Wilking/Reuters)

The fight over which cellphone carrier has the best unlimited data offering isn't over. AT&T announced late Sunday that it is debuting two new unlimited plans this week — one, a no-frills option that tries to undercut its rivals on price; and the other, a more expensive plan with all the bells and whistles.

Both plans will become available Thursday.

The no-frills option, and how it stacks up

The cheaper plan, Unlimited Choice, costs $60 per month for a single line (or $40 a line for a family of four), as long as you have autopay and paperless billing enabled. While that reflects a price cut over AT&T's current unlimited plan ($100 for a single line or $45 a line for four), it does come with limitations.

Most importantly, the Unlimited Choice plan tops out at a maximum download speed of 3 Mbps. That's fast enough for mobile browsing, email and other basic applications, but it means no high-definition video streaming; AT&T says videos will be limited to standard definition. And the plan also lacks the ability to extend your phone's Internet connection to other devices, such as a PC or a tablet.

In comparison, T-Mobile and Verizon's plans both offer high-definition streaming and 10 GB of mobile hotspot tethering as standard features in their unlimited plans, whereas AT&T Unlimited Choice does not. Sprint offers 5 GB of tethering data and restricts online video to SD quality, along with a few other limitations.

For a single line, AT&T's Unlimited Choice plan is the same price as Sprint's unlimited plan, $10 a month cheaper than T-Mobile's, and $20 a month more affordable than Verizon. At four lines, those price differences appear to diminish, though it's important to point out that T-Mobile includes taxes and fees in its advertised price rather than tacking them on as extra items on your bill, whereas the other carriers do not.

The premium package

AT&T's more expensive unlimited plan, Unlimited Plus, is essentially Unlimited Choice but allows for HD video streaming and includes 10 GB of tethering data. Once you use up the 10 GB of tethering, your speeds will be slowed. This high-end package costs $90 a month for a single line or $46 a month for four.

By that measure, AT&T's price for a single line is still more expensive than that of any of its rivals, though the four-line price is comparable to Verizon's.

AT&T hasn't given up trying to get consumers to buy cellphone and TV service as a bundled package. The company is dangling a discount of $25 a month on TV service if you sign up for both Unlimited Plus and one of AT&T's television services.

Some may remember that AT&T previously made buying DirecTV or U-verse TV a requirement for unlimited plan customers; the company recently scrapped that and made it possible to buy unlimited data without TV. But by attaching a video discount to its higher-end unlimited data plan, AT&T appears to hope that enough people who are attracted by HD streaming and tethering will be motivated to pay just a bit more for television, too.

As before, both Unlimited Choice and Unlimited Plus may put restrictions on your download speeds if you use more than 22 GB of data in a single month.