HDMI devices are manufactured to adhere to various versions of the industry specification, where each version is given a number such as 1.0, 1.2, or 1.3. Each subsequent version of the specification uses the same kind of cable but increases the bandwidth and/or capabilities of what can be transmitted over the cable.
Hdmi 1.3 added the ability for DeepColor, TrueHD and Master HD audio formats. The only difference between HDMI 1.3a and 1.3b is that 1.3b implemented stricter compliance standards for the manufacturers. If you have no DeepColor or Master HD audio sources (and if you're not sure if you do then you probably don't), then the expense of 1.3b cables may not be worth it right now. You may see cables say they are HDMI 1.3b certified. All that means is that they have undergone the 1.3b testing standards.
For example the previous maximum pixel clock rate of HDMI interface was 165 MHz which was sufficient for supporting 1080p at 60 Hz and WUXGA (1920x1200) at 60 Hz. HDMI 1.3 increased that to 340 MHz which allows for higher resolution, such as WQXGA (2560x1600), across a single digital line. An HDMI connection can either be single link (Type A/C) or dual link (Type B) and can have a video pixel rate of 25 MHz to 340 MHz for a single link connection or 25 MHz to 680 MHz for a dual link connection.
For consumers, there is no difference between HDMI version 1.3 and 1.3a or 1.3b. These minor revisions to the specification typically relate to manufacturing or testing issues and do not impact features or functionality. In addition, HDMI Licensing, LLC is actively working with manufacturers to reduce confusion for consumers by de-emphasizing version numbers and focusing instead on product features and functionality.
Focus more on getting Category 2 Certified cable as this will better ensure that more data will arrive across longer (greater than 5m) distances and your TV will have to do less correction giving you a clearer picture. The Category 2 grade transfers data up to 10.2 Gbps . . . plenty fast for true 1080p.