I assume you are talking about the new water you are using for water changes? If yes, I have used both methods you mention.
I have a number of large water storage tanks in the insulated crawlspace under half of my house, which allow water to warm up to ambient temperatures for a change. An airline in each tank keeps the water temperature even throughout, and water feeds by gravity to the aquariums. Some of the storage bins have heaters in them to provide water at warmer temperatures for tanks that require that.
This method works really well, but in my case I didn't have the storage capacity to do all my water changes all on the same day. I reasoned that a tankless system was the answer, so recently installed one. It's finicky to get it just right; various models require various flow rates to operate properly, and all are designed to produce hot water for washing, etc. To get one to provide you with water temperatures at a usable level for fish tanks takes a lot of trial and error. I'll be honest; I'm a dyed-in-the-wool DIY-er but I was totally at sea with this thing; fortunately a good friend who is an industrial plumber helped me out and even he was a bit puzzled by the project. We got it all hooked up and running eventually, but it took multiple trips into town and multiple internet orders to get everything set up, with lots of dead ends and false starts.
Now it's up and running, and it does what it is supposed to do; supply a continuous supply of water at a certain temperature...although getting it to supply that particular temperature was a horror show. And I'm still not completely in love with it, simply because it provides only that one temperature, in my case 72F. I have a couple tanks that I prefer a bit warmer, so I still store water and pre-heat it for them. And I have several that require cooler water, at least at some seasons, so the water for them still needs to be stored to ambience.
The remainder of my tanks are just fine at 72F, so I can now do all my water changes on the same day, but it isn't the seamless process I had envisioned. After all the jumping through hoops to get a consistent 72F, I wouldn't dream of trying to alter it even a few degrees and risk losing my place and starting all over again.
So your choice would be influenced by several factors: willingness and ability to do the plumbing, amount of space you have available for storage bins, cost considerations of the installation (tankless heater + plumbing + pressure balancing valve + electrical work + incidentals will likely cost far more than a few storage bins), etc.
I'd say that if you have the room for the storage tanks, and if the ambient temperature where you store them is close enough to the desired aquarium temperature, that this method is preferable. If, on the other hand, you are considering switching your entire house over to a high-capacity tankless system, then doing the extra work of plumbing hot/cold water lines to your fishroom and installing a pressure-balancing valve might be preferable. I would never suggest that someone go the route that I did, i.e. get a small tankless unit and devote it to supply water strictly for aquarium use.