The largest x^y+y^x occurs for y=x which for a given x-range occurs for the largest x in that range. Thus, the largest Leyland number up to x=13000 is 2*13000^13000, which has 53482 decimal digits. Here is a table of Leyland number decimal digits for largest x from 13000 to 30000 at intervals of 1000:

13000 53482

14000 58047

15000 62642

16000 67267

17000 71918

18000 76596

19000 81297

20000 86021

21000 90767

22000 95534

23000 100321

24000 105126

25000 109949

26000 114790

27000 119648

28000 124521

29000 129410

30000 134314

This will give you an idea of where the overlap between the two systems lies. Having checked all Leyland numbers smaller than (currently) 84734 decimal digits implies (barring errors) that I have checked all x smaller than 19728. That allows me to suggest that

this table of x, y values (based on Andrey Kulsha's ordering) is complete. Of course it would be nice to have verification.