Braking feel is largely tied to brake fluid and friction materials. Cars that are 20 years old are not using the original stuff for any of that.
ABS does not help you stop sooner. It really doesn't and it's not supposed to. Seriously, it's to help you turn while stopping. In a straight line, you're often better off without it.
The current generation Civic has a torsion beam rear suspension, while the old ones like your '88 had a double-wishbone setup. It doesn't handle as well as the old ones. I wasn't making that up, believe it or not. Your '88 Civic was essentially a front-wheel drive sports car and competes on that level even today.
As for that Top Gear episode, there were a few matchups where the older car did a lot better than the modern equivalent, but yeah, as a rule, most newer cars are better than their equivalents 20 years ago.
Consider that my response was toward someone who made the flawed assumption that a car now will be less likely to hit that barrier because it will handle better, but the truth is that a modern car will not necessarily handle better and will be heavier. A heavier car inherently can't turn or stop as well as a lighter car. It's a flawed assumption.