Even on a waypoint relatively close, you can get 1 minute, sometimes 2, of difference between ND and MCDU.
ND indeed looks at the ground speed, while MCDU make predictions based on last overhead waypoint wind (stored), blending with actual for the current waypoint estimate.
Even when the clock time from GPS and MCDU are identical, the MCDU will round up to the next minute past 30 seconds. So 10:39:32 will show as 10:40 in the FMS predictions.
The ND will use time without rounding up, so 10:39:59 will show as 10:39 on ND predictions. It is the same on the lower ECAM, the time displayed will wait past 59 seconds to switch to the next minute, you can easily compare with GPS clock on the right.
For the MCDU predictions, it can be seen when selecting vertical revision, then RTA. The time predicted to the waypoint will be displayed with the seconds. If it shows 10:39:29, then the FPLN page will display 10:39. If it shows 10:39:30, the FPLN will display 10:40.
Since the ND and FMS do not use the same references for their predictions, if the ND prediction is 10:38:59 and FMS 10:39:31, then the difference should be 2 minutes.
I guess this is the last proof to date that pilots have really nothing to do but sit on their hands, while the bean counters make the company work!
Flex