Our freshly kegged Amber German Lager has a lingering bitterness (Mt. Hood), not unpleasant, but very perceptible. The water (filtered tap) had a moderate calcium content with other minerals.
The Amber Czech Lager has a very soft bitterness (Saaz), not nearly as pronounced. The water was a 50/50 split, RO and filtered tap water.
How much does the water profile impact the perceived bitterness level?
Was the water the same for both batches? If you added calcium sulfate or calcium chloride to the batches were the additions the same for both batches? Higher sulfate levels can produce a crisper, drier beer and at some point that crispness can reach “harsh” levels. It could be the hops as Denny mentioned and it can also be the number of IBUs you got from your bittering addition in both of the batches. Sounds like more information is necessary. I have forgotten to add CaCl in the past and my water is already higher in sulfate than it is in chloride… so I got a very crisp, dry finish in that beer. You could also add more bittering hops than you wanted, possibly. I had a brew bud who was using his scale and got his “grams” and “ounces” mixed up. Whoo boy.
Assuming it is due to the water, it could be reduced sulfate from dilution. Does your tap water use chloramine and if so are you removing it? Chlorophenols have a lingering aspirin-y bitterness and would also be reduced by dilution.
But like Denny says, there are too many variables here to do more than guess.
I’m less concerned with the mineral content and more concerned with pH. High pH can leach bitter components from the grist and increase the extraction and conversion of hop bittering.
Typical tap water will require acidification for brewing pale beers.