"Storing" electricity using H2 is relatively straightforward: use electricity to electrolize water and get H2 (and O2), store the H2 (presumably liquefied) and then burn it to either generate electricity again or to power existing energy-intensive processes (e.g. smelting iron ore). Not sure how efficient the electricity -> H2 -> electricity conversion is, but ok...
Now, if you use methanol, you get the H2 like before, then "make it react" with CO2 (and CO2 is not really eager to react with anything IIRC) to get methanol, and then you burn it, getting CO2 which has to react with more H2 or otherwise you wouldn't be carbon neutral. Sounds to me like this process can only be less efficient (and more complicated) than the H2 process? Potentially much less efficient and much more complicated?