The fastest residential Internet service in the US is Comcast Cable 105 Mbps. It is only available in select locations and it is very expensive.(several hundred installation fee and over $100 monthly) Comcast has many other speed tiers with lower prices, most of which will be much faster than your old At&t DSL package.
If you had At&t DSL over standard copper phone lines, your speed was most likely in the 1.5 to 6 Mbps range.
At&t offers fiber optic DSL (U-Verse) in some areas that has speeds up to 50 Mbps. Verizon also offers a similar fiber-optic Internet (FiOS) in some areas.
As far as DSL vs Cable Internet goes,
DSL (Digital Subscriber Line) is a form of broadband Internet that is transmitted over standard twisted pair copper telephone lines. DSL speeds range from 256 Kbps to 12 Mbps depending on distance from the telephone company and plan that you purchase. Newer ADSL2+ fiber optic services can be as fast as 50 Mbps. http://en.wikipedia.org/wiki/Digital_Subscriber_Line
Cable Internet is a form of broadband Internet transmitted over coaxial television cables. Cable Internet speeds range from 1.5 Mbps to over 100 Mbps using newer DOCSIS 3.0 technology. The speed of the service depends on your exact area and service package that you order. http://docsiscablemodem.com/
DSL is limited by the distance from the CO or telephone companies central office. The copper limits are around 15,000 feet. and this would be the actual length of the cable not the point to point distance. If your neighborhood has fiber optic this distance can be extended,
For higher DSL speeds these distances get shorter, the faster the speed the shorter the distance. A 3 Mbps DSL connection would be about a maximum of 6000 feet from the CO. If you exceed these limits quality and speed will suffer.
A lot will depend on what Internet providers are available in your specific area, and what levels of service they offer in that location.
For instance DSL Internet might be better in one part of the city, and cable Internet options better in another. DSL is generally cheaper than cable Internet, however the cable plans are usually faster.
If you are interested in high speed Internet then go to a ISP comparison site that lets you input your address, http://isp1.us/find/ and compare the pricing and terms of the offers that are available in your exact area.
The physical address is needed because some services, particularly DSL, are very distance sensitive. For example you might be able to get a specific level of service while your next door neighbor can't.
You'll want to pick the fastest plan that fits your budget. In some areas this can be 100 Mbps+. But these high end broadband plans are expensive. You may find that something in the 5 to 30 Mbps range might satisfy your needs at a much lower cost.
Choose the best one for your Internet usage and budget.
Good Luck...