10 years ago I would be hesitant to compare battery and petrol units to each other as there was a significant difference in power and runtime. Given the advancements in battery and motor technology such as higher amp-hour cells and brushless systems, I am more than confident you will be exceptionally happy once you make the switch to battery-powered garden tools.
The equivalent to petrol machinery in the battery range is the 36V system of Ryobi tools, the 58V system in AEG tools or the 82V system in Victa tools. Don't let the voltage confuse you, 82V doesn't indicate the tool is any more powerful than a 36V unit.
If you would like to achieve a similar capability to petrol machines I would strongly suggest going with the highest amp-hour battery available for the units. In the Ryobi range that would be the Ryobi 36V 5.0Ah Hi-tech Battery. Amp-hour refers to the runtime on the unit. It will be most economical to purchase a unit that comes with the higher amp-hour battery. Buying the battery separately can be a significant investment.
The initial investment into a machine that comes with a 5.0Ah battery can be seen in the runtimes produced. A lawnmower with a 5.0Ah battery could run for over an hour, the same machine on a 2.5Ah battery may run for 30-40mins. If you need to purchase a secondary 2.5Ah battery to switch out completing the job, you could now be over the cost of the initial larger battery kit.
The Ryobi expand-it edger attachment will fit onto a 36V Ryobi line timmer unit and I believe it will do a similar job to a petrol unit. The only time I suspect you would notice the difference between a battery lawnmower and a petrol lawnmower is in the runtime and if you go on holidays for 4 weeks returning home to find knee-high grass. A battery lawn mower will need to reduce that down in a couple of cuts, one at full height and a second finishing cut. In saying that though, most petrol lawnmowers will bog down when they hit a thick patch of tall grass as well. - MitchellMc
One thing I will add though concerning the battery amps is their respective weights. There is quite a difference between the weight of a 1.0Ah and 5.0Ah. With the mower that isn't going to be an issue, but with the whipper snipper it really is a serious consideration especially if you are older or have any upper body injuries/issues.
This can also change from model to model and brand to brand as it also comes down to how the tool is weighted and if it is distributed effectively or not. That was one of the main reasons I switched to a battery trimmer, the reduced weight has been much better on my neck and back. - hutchjnr