A lot of the perception that the Russians are stricter, in my opinion, derives from the fact that the Russian Church Abroad was a "traditionalist" Church up until recently. Therefore, they kept more of the older, stricter piety than the "modernist" churches, like the New Calendar Greek Church. But I've been to Greek Old Calendar churches, like St Mark of Ephesus in Roslindale, MA, and they are on the whole just as strict and pious as the Russians, e.g. standing through the whole Liturgy. St Markella's in Astoria is a bit of an oddball, since most of the congregation there are former New Calendarists, so they're somewhat less strict, e.g. in the formality of their dress for liturgy, whether the women cover their heads, not standing through the whole service etc. The older Old Calendarist core of the congregation I observe to be more strict, e.g they're the ones who make a real effort to make it in time for Sunday morning Orthros, or at any rate before the Liturgy begins, to stay on their feet as much as they can bear, and so on.
Aside from this, there are some real differences in the two traditions. E.g. the Greeks have a custom of kneeling through the whole Epiclesis on weekdays, while the Russians stand and make a prostration at the end. But these are fairly minor differences. Someone noted that in fact the Russians have for a long time observed the traditional fasting rules more laxly, e.g. the ban on oil is mostly a dead letter even in very pious households. Again, the perception that the Russians are stricter in fasting seems to come from the fact that they remained more traditional in general, and therefore continued to observe the fast days long after most Greek New Calendarists stopped doing so.