The OP was clear here. He said the most accomplished, which means that I won't speculate on the quality of the competition. This will be simply based on accomplishments. And I'm running this through Wimbledon of their age-20 seasons.
Total slam titles sits at 2 each. This is a wash. Nadal leads 3-2 in slam finals. Alcaraz leads 4-3 in slam quarters. I'm giving Rafa the edge here with the extra slam final. The rankings points would do the same, since I believe that a slam final is worth 1200 points while a slam semi + slam quarters=360+720=1080 points.
Total titles: 17-13 Rafa. Big edge to Rafa
Masters titles: 6-4 Rafa. Solid edge to Rafa
World #1: Alcaraz hit world #1 and Rafa didn't. This is nearly an equalizer here. World #1 is huge.
Overall Record(per Tennis Abstract):
Rafa: 167-44, .791
Alcaraz: 137-35, .797
Their winning pct is nearly identical. But Rafa has 30 more match wins. Edge to Rafa.
Record vs top 5
Rafa: 9-5, .643
Alcaraz: 10-6, .625
Record vs top 10
Rafa: 17-7, .708
Alcaraz: 20-10, .667
Their records vs top opponents is a wash to me. Rafa has the better winning pct, but Alcaraz is close and has more wins.
Nadal would be ahead by a decent margin, if we ignore weeks at #1. This is a huge thing for Alcaraz. Now granted, there is a TON of context regarding world #1 and the opponents. But the OP was clear about this. This is about pure hardware and accomplishments, not context or speculation.
I'm giving this to Alcaraz. Hitting world #1 is just too big here.