Among players who have faced them at least 10 times altogether.
The first name that came to me was Dominic Theim. He is 16 wins to 18 losses, so his wininning percentage is very close to 50%. Is there anyone else who has a good record against Big 3 as a whole?
Medvedev? Zverev? Nishiokori? Tsitsipas? Murray? Berdych? Cilic maybe?
I think Thiem is the clear #1 here. Such a shame what happened to him.
Among players with >10 matches against the Big 3, the top 5 are:
1. Thiem
2. Zverev
3. Nalbandian
4. Murray
5. Coric
Below are the percentages of the players you asked about, in order of win %.
Zverev: 11-17 (39.3%)
Federer 4-3
Nadal 3-7
Djokovic 4-7
Murray: 29-56 (34.1%)
Federer 11-14
Nadal 7-17
Djokovic 11-25
Medvedev: 6-17 (26.1%)
Federer 0-3
Nadal 1-5
Djokovic 5-9
Tsitsipas: 6-20 (23.1%)
Federer 2-2
Nadal 2-7
Djokovic 2-11
Berdych: 13-65 (16.7%)
Federer 6-20
Nadal 4-20
Djokovic 3-25
Nishikori: 7-38 (15.6%)
Federer 3-8
Nadal 2-12
Djokovic 2-18
Cilic: 5-36 (12.2%)
Federer 1-10
Nadal 2-7
Djokovic 2-19
Six more honorable mentions with win percentages around 30%:
Nalbandian: 11-20 (35.5%)
Federer 8-11
Nadal 2-5
Djokovic 1-4
Coric: 5-10 (33.3%)
Federer 2-4
Nadal 3-2
Djokovic 0-4
Kyrgios: 6-13 (31.6%)
Federer 1-6
Nadal 3-6
Djokovic 2-1
Hewitt: 14-31 (31.1%)
Federer 9-18
Nadal 4-7
Djokovic 1-6
Tsonga: 16-39 (29.1%)
Federer 6-12
Nadal 4-10
Djokovic 6-17
DelPo: 17-45 (27.4%)
Federer 7-18
Nadal 6-11
Djokovic 4-16
If we look at players with fewer than 10 matches, four actually have better win rates than Thiem, but only one of them (Hrbaty) has faced all three. Rublev also has a decent record. There might be others I am missing here.
Corretja: 5-2 (71.4%)
Federer 3-2
Nadal 2-0
Djokovic 0-0
Brown: 2-1 (66.7%)
Federer 0-0
Nadal 2-0
Djokovic 0-1
Hrbaty: 5-3 (62.5%)
Federer 2-1
Nadal 3-1
Djokovic 0-1
Vesely: 2-2 (50%)
Federer 0-0
Nadal 0-2
Djokovic 2-0
Rublev: 3-5 (37.5%)
Federer 1-0
Nadal 1-3
Djokovic 1-2
There are also players who have a winning h2h against Federer and have never played Nadal or Djokovic (like Kafelnikov, Rafter, and Kuerten), but I don't think they should be listed here if they have only played one of the three.