I was having the exact same issue the OP was describing. After reading dozens of threads for this game describing this issue, I'm very surprised no one posted a proper detailed explanation of what is wrong and how to fix it.
Using ePSXe, Tekken 3 freezes/crashes after completing arcade mode but before the credits movie is supposed to start. The announcer saying "King of Iron Fist Tournament, Enter the Tekken" is the last thing that happens and the screen remains black. I use the NTSC release of Tekken 3 which has 3 .bins (Track 1, 2, and 3) and one .cue.
I'm almost 100% certain the issue is the fact that the game is multi-track and ePSXe (at least every version after 1.4) does not have proper multi-track support. This is not an issue for the vast majority of games but in the case of Tekken 3 it is. And sure enough after mounting the .cue using PowerISO, "Track 2" is the ending credits song. To fix the issue you need to create an image that merges all of the tracks into one .bin.
I first tried this with PowerISO since this was the tool I had installed on my computer but there was a problem. After creating an image with the source being the .cue mounted on a virtual drive, I launched the new .bin that was created. I was able to make it to the credits and the game did not crash but the song for the credits was corrupted. It sounded like data and horrible scratching noises. Obviously "Track 2" and "Track 3" were not converted correctly.
I then used ImgBurn v126.96.36.199, with the original .cue mounted using Daemon Tools Lite v4.35.6 (since a virtual drive created by PowerISO is not recognized by ImgBurn for some reason), to create the image. I tested the image created by ImgBurn and it works as it should. The game does not crash and the credits song plays and sounds correct.
A big thanks to this post as it was the reason I tried ImgBurn and Daemon Tools Lite:
Only use ImgBurn v188.8.131.52 or below because I tried using v184.108.40.206 and the process of creating the image was stuck at 0% due to an infinite loop at "File Splitting: Auto". More information about the problem can be found here:
Make sure you use Eternal SPU or you will likely not hear the credits song. I found that P.E.Op.S. DSound SPU v1.9 and P.E.Op.S. Sound SPU v1.10b do not play the credits song.
Just to add more information about my experiences, I tried SSSPSX v0.0.34 and the emulator seems to have at least partial multi-track support because the game does not crash and the credits play. But the credits song does not play, regardless of the SPU used.
Last but not least, PCSX-R has native multi-track support. So Tekken 3 can be played using PCSX-R without having to convert the multi-track .bins into a single .bin. I tested PCSX-R myself and indeed the credits and credits song play with no issues.