QED Digit battery supply

I have been using a couple of 12v lead acid batteries to power a modified Quad 33 pre amp and a QED Digit which has been modified for 2 separate power supplies. The batteries are automatically switched over to smart chargers when not in use, and one powers the Quad while the other powers both sections of the Digit. The Quad battery is 3.2ah and the other is 2.8ah, and is getting on a bit - my question is, should I have separate batteries for each section of the Digit, or, if not necessary, what would be the recommended size for a single?
 
I'm not sure of the current draw - I can't find any specs on the Digit, but I assume it's not huge. The 2.8ah battery has been fine supplying both sections for several hours at a time, but it is now probably between 10 - 15 years old and no longer holds a charge for very long. In the past it was never drained during ordinary listening sessions. When it's not in use it is switched over to an automatic charger which bulk charges if necessary, and then maintains a float charge rate. It has earned its money, so I'll replace it, but I'm wondering if there is any advantage in having two, maybe smaller, batteries, one for each section. As far as I know it's a regular Yuasa general purpose lead acid - NP2.8-12
 
Point taken - thank you. I doubt that I'd notice a difference unless it was huge, and the modification had been done before I bought it so I have no point of comparison. I suppose that connecting the two separate parts to the same supply, battery or otherwise, is the same as not splitting them in the first place. I started by using a battery for the preamp ages ago and I've been very happy with it. It seemed to be an easier and cheaper way to avoid noise than alternatives, so I went with it when I got the DAC too. I could do a quick trial with a motorbike battery (I have a few....)