I decided to take advantage of the PCGS Crossover special ending April 30, 2015 (only $10 fee if a coin does not crossover, instead of the usual $30).
As a variety hunter, I accumulate varieties in all sorts of TPGs and all sorts of conditions. So I sent 40 graded coins to PCGS and crossed my fingers. The order took 2.5 months.
The results of this experiment, and some observations/comments are below. Some coins had gone through 2 or 3 grading companies previously, all those are listed. (DNC = Did not cross):
1. 1859 1c DP9 No.1 ICCS EF40, ICG AU53 - PCGS AU53
2. 1859 1c DP9 No.2 CCCS MS62 - DNC (old cleaning suspected on a portion of the reverse, retoned)
3. 1859 1c DP9 No.3 ICCS EF40, CCCS EF40 - PCGS AU53
4. 1859 1c DP9 No.3 ICCS EF40, ICG AU50 - PCGS AU50
5. 1859 1c DP9 No.3 ICCS AU50, ICG AU50 - PCGS AU53
6. 1859 1c DP9 No.4 ICCS AU50, CCCS AU50 - PCGS AU55
7. 1859 1c DP9 No.5 ICCS VF30, CCCS VF30 - PCGS EF40
8. 1859 1c TP9 ICCS VF20, ICG VF35 - PCGS VF35
9. 1859 1c TP9 ICCS EF40, CCCS EF40 - PCGS EF45
10. 1859 1c TP9 NGC AU55 - DNC (old cleaning suspected, possibly lacquered, retoned long ago)
11. 1859 1c 9/inverted 9 ICCS EF40, CCCS EF40 - PCGS AU50
12. 1859 1c W9/8 ANACS AU55 - DNC (very light hairlines)
13. 1894 1c Thick 4 ICG MS63 - PCGS MS63
14. 1858 5c Large Date ICCS AU50, ICG AU58 - DNC (light hairlines)
15. 1858 5c Large Date CCCS AU55 - PCGS AU55
16. 1885 5c L5/5 ICCS MS62, CCCS MS62 - PCGS MS62
17. 1886 5c S6 ICCS MS60, CCCS MS60 - DNC (light hairlines)
18. 1858 10c 1st 8/5 ICCS AU55, CCCS AU55 - PCGS AU55
19. 1870 10c N0 0/0 ICCS MS64, CCCS MS65 - PCGS MS64 (ouch, but finest known)
20. 1886 10c Pt6 ICCS AU50, CCCS AU50 - PCGS AU55
21. 1892 10c S9 ICG AU58 - PCGS AU58
22. 1858 20c ICG MS60 - PCGS AU58
23. 1880 25c N/W0 NGC EF45 - PCGS EF45
24. 1886 25c 6/7 ICCS EF40, CCCS EF40 - PCGS EF45
25. 1906 25c Small crown ICCS VG8, ICG VG8 - PCGS VG10 (WOW!)
26. 1936 25c Dot NGC AU55 - PCGS AU55
27. 1936 25c Bar SEGS MS63 Pittman - PCGS MS64 (WOW!, but lost the Pittman Name on the Slab)
28. 1872 50c ICCS AU58, CCCS AU58 - DNC (not sure why, maybe AU55?)
29. 1900 50c ICCS AU58, CCCS AU58 - DNC (questionable colour - beautiful toning that goes into shades of purple)
30. 1900 50c NGC AU58 - PCGS AU55
31. 1900 50c ICG AU58 - PCGS AU58
32. NF 1882 20c ICG AU53 - DNC (light hairlines)
33. NF 1888 20c ICG AU58 - PCGS AU55
34. NF 1885 50c ICG AU50 - PCGS EF45
35. NF 1898 50c SW ICG AU50 - PCGS AU50
36. NF 1898 50c LW ICG AU58 - PCGS AU55
37. NF 1899 50c ICG AU58 - DNC (moderate hairlines, I should have known better but decided to test the waters anyways)
38. NF 1917C 50c ICCS MS64, CCCS MS64 - DNC (not sure why, maybe it was a MS63, my cutoff was MS64)
39. NB 1864 5c L6 ICCS AU50, CCCS AU50 - PCGS AU55
40. 1870 25c 5/5 ICCS AU50, CCCS AU50 - PCGS AU55
To summarize, 30 of 40 coins crossed over. The most common reason for coins not crossing over was light hairlines. These could be found in ICCS, CCCS, NGC, ICG or ANACS holders. PCGS seems to be the most strict
TPG regarding any hairlines, even very light ones.
ICG and NGC grades run similar to PCGS. I didn't have enough ANACS coins but I would expect the same.
Biggest pleasant surprise was PCGS upgrading two ICG coins (including a 1906 small crown) and even a SEGS coin!! I had mixed feelings about the 1936 25c bar going from SEGS MS63 to PCGS MS64

but losing the Pittman label

...oh well, you can't have it all.

ICCS and CCCS will upgrade 5-10 points in PCGS in the VF-EF range, on a fairly regular basis.
However, anything goes in AU50+. Several ICCS/CCCS AU58s didn't cross over to PCGS and I wasn't sure why.

Overall, I was very happy with the experience, although the order took FOREVER, and with a dozen calls into PCGS, their customer service are truly lame ducks (they will say they have NO idea what's going on with your order and there is nothing you can do but wait). But for the added market value, the hassle was totally worth it.