Both Gregorian and Julian computations are based on the same equation:
235 synodic lunar months = 19 Julian years + correction.
The Julian computation set the correction to zero. This gives an average synodic lunar month of 29.530851 days.
The Gregorian computation sets the correction to 8 days in 2500 Gregorian years. When averaged over many cycles,
this gives an average synodic lunar month of 29.530587 days.
The astronomical value is currently 29.530589 days, and is slowly (very slowly) decreasing in terms of contemporary mean solar days. (In Claudius Ptolemy's time it was around 29.530594 days). So the Julian value is presently too long by .000262 days per lunar month or about a day in 309 years. The Gregorian value is too short by .000002 days per lunar month, or about 1 day in 40,226 years.
Whether or not setting the correction to a value other than zero constitutes a "difference in methodology" depends on one's definition of "methodology". The observed differences between Eastern and Western Easter are (as someone has already noted) due to the accumulation of errors in the Julian calendar over the centuries, creating what is now a large systematic error in the Julian tabular equinox and the Julian tabular lunar phases, relative to the astronomical phenomena they were originally intended to approximate.
For convenience of future reference by those posting to this thread, here is the full 19-year list of paschal full moons for both systems. Easter, Eastern or Western, is the Sunday after the Paschal full moon. (Yes, it's really that simple!) The Gregorian column is valid until 2200. The Julian column is valid until 2100. The present year, 2013, is the 19th and last year of the cycle according to the numbering system used here. Next year, 2014, will be the first year of a new 19-year cycle.
Gregorian date
Year of cycle | Gregorian PFM | of Julian PFM (νομικον φασκα)
------------- -------------- ---------------
1 | April 14 | April 18
2 | April 3 | April 7
3 | March 23 | April 26
4 | April 11 | April 15
5 | March 31 | April 4
6 | April 18 | April 23
7 | April 8 | April 12
8 | March 28 | May 1
9 | April 16 | April 20
10 | April 5 | April 9
11 | March 25 | April 28
12 | April 13 | April 17
13 | April 2 | April 6
14 | March 22 | April 25
15 | April 10 | April 14
16 | March 30 | April 3
17 | April 17 | April 22
18 | April 7 | April 11
19 | March 27 | April 30