Here it goes, i've been to all places.
Both airport->train connections aren't very easy, but from HEL it's easier and more calm as HEL isn't so busy as LED.
If you decide to fly to HEL, you have to transfer to the central station in Helsinki (busses run between both regurlary) and from there it takes you about 4 hours or so and the international train goes something like 3 times/day. At about 7.30AM and at 3.30pm &6.30. (just check www.vr.fi)
If you decide to fly to LED, then you have to travel from the airport in the south of the city to Finlyanski railway station (center-north) (which is at the metro station Ploshad Lenina). From there it takes you about 2 hours, and you can take the train to Helsinki from there, or a local one (bad quality).
I'd go for HEL as most major airlines also run higher frequencies there.
Btw, Finnair also flies to some smaller airports in the east of Finland from where Vyborg is even easier reachable. Also Ryanair flies to LPP.
Всяк глядит, да не всяк видит.