Also, the Finns never actually invaded Russia during the Continuation War. They just took back what was theirs before the Winter War.

Another pedantic comment, but they actually went beyond their former borders to create a small buffer zone. And in the north, German units based in Finland went into Soviet territory in an attempt to cut the Murmansk railway.

Even so, the very restricted conduct of Finland during both conflicts made it clear that they only had defensive intentions in mind. If Finland had taken a more aggressive stance and coordinated their actions more fully with Germany's, there's little doubt that Leningrad would have fallen no later than 1942—a possibly war changing scenario.

Instead, because Finland refused to cooperate fully, Leningrad tied down a substantial number of Axis forces for years, thus excluding them from the more fluid and consequential events farther afield. In the vitally important months leading up to the Soviet's counterstroke at Stalingrad, the lack of Finnish support influenced the German High Command's decision to begin transferring the newly freed 11th (?) Army and other various units from the recently subdued Crimea northwards to Leningrad. This move couldn't have come at a worse time as it coincided with the vastly expanding Southern Front becoming increasingly overextended, and the order eventually had to be rescinded to prevent a complete rout of these forces in the wake of the Soviet's Stalingrad offensive. If Finland's recalcitrance hadn't prompted the shifting of these forces northwards and instead seen them turned into an operational or strategic reserve for the South, it's very likely that Soviet's "Operation Uranus" would have been no more successful than its sister operation "Mars" against A.G. Center; even if German forces nevertheless became surrounded in Stalingrad, these substantial reserves could have ensured that it did not deteriorate into a situation any more serious than the preceding Demjansk pocket—a German protrusion that eventually turned into an isolated "kessel" during the Soviet winter offensive of 1941, but was successfully resupplied by air during its months long entrapment until its final relief by coordinated actions of German units both inside and outside the pocket in the spring of 1942.

Additionally, Leningrad's continued resistance offered psychological benefits to the Soviets and remained a rallying point for them up until and beyond the eventual lifting of the siege. For these reasons some people wonder if it is even accurate to consider Finland an ally of Germany during the first years of the war, and instead prefer to connote it with the status of co-belligerent.

In the end though, although reality played out reasonably favorable for Finland, I would be tempted to posit that it would have been in Finland's best interests to cooperate more fully with the Germans; Bulgaria, who despite being a member of the Axis Pact maintained a strict neutrality with the Soviet Union and never declared war on or sent forces against it, was nevertheless invaded by the Soviet Union when it swept through the Balkans in late 1944. Even if Finland had not even attempted to regain its newly lost territories, I doubt its ostensible neutrality would have deterred the Soviet Union from eventually either arm-twisting Finland into agreeing to unpalatable terms (such as a substantial increase in Soviet forces stationed in Finland—previously isolated to a few small islands, and, if I recall, possibly a small detachment in Helsinki—and use of airstrips, ports, et cetera) or opportunistically invading, at least in part, the country to preempt any actions by Germany, secure certain strategic locations, or to put pressure on German-occupied Norway.

Finland's success may have owed a lot to adroit politicking and maneuvering on the part of Mannerheim, but I still think most would agree that Finland's status as being the only former Russian territory to escape reincorporation into the Soviet Union was largely due to a streak of serendipitous luck—although that didn't mean Fate went easy on them! I just believe that sometimes to ensure one's freedom and independence, one must make proactive decisions instead of constantly trying to parry others actions.