In both cases, daily calorie deficit is equal. Calorie intakes and TDEEs are different.
In which case I would feel better?
Case 1: [Calorie intake of 0.8*BMR] and [doing exercise]
Case 2: [Calorie intake of BMR, or more] and [doing more exercise]
PS: I think It wouldn't matter if the deficit is low. But I'm working on increasing it.
Generally it's much easier to, for example, skip eating a banana than to go out jogging for fifteen minutes. Personally I feel it's even more so when your caloric deficiency is more than 500 kcal per day.
This is all just anecdotal, so I'd try it out myself if I were you. But for myself I'd just do some heavy lifting to maintain muscle and then cut the bulk of the calories at the intake instead.
You are asking a question specific to the way that exercise would make you feel. Everyone is different, this includes their body's ability to respond to different stimuli and their emotional response to changes made to routines. Other people's experience may have similar, or no similarity, to what you will feel.
Your best bet will be to try the different routines you suggest for a short while and note down the pros and cons of both, how they make you feel and whether you will be able to maintain the routine for long.
However, it must be said that exercising is a lot harder work than not taking in the calories in the first place. Running for a half hour for a normal person might burn 200 calories. Or one could just eat lighter. So my suggestion would be that case 1 would probably be the most sensible option for most people. And that you can then adapt the routine according to your notes (as I suggested) to see how much extra exercise, and how much less food, you can eat.
