This survey (PDF), commissioned by the Advisory Board for Defense Information, has the goods.
Half of the respondents answered a multiple-choice question and the other half filled in an open question.
The most important (48 %) reason for remaining outside NATO is to prevent Finnish troops from having to fight foreign wars. The second most important (46 %) reason is that Finland should not be involved in great power conflicts. The third (43 %) reason is the disproportionate dominance of the United States in NATO. The fourth most often (40 %) cited reason was that Finland's NATO membership could increase the threat of Russia against Finland.
As for the open answers, the reasons were analogous. The most often used arguments against military alignment were that NATO membership was thought to increase the threat of Russia against Finland (N=68) and that Finnish "sons and grandsons" would be forced to fight foreign wars (N=51). The justifications also included increased insecurity (N=32), expenses (N=32), the irrelevance of NATO (N=30), the importance of maintaining independence and sovereignty (N=22) as well as the superiority of non-alignment (N=27).
The most important reason for backing NATO membership was that the Finnish Defence Forces were not considered capable of defending Finland on their own (53 %), followed by obtaining military security against Russia (45 %), benefits from participating in western organizations (40%) as well as the opportunity to participate in decision-making with regard to NATO operations (38 %).
The open answers brought increased security (N=78) to the forefront, followed by obtaining support if Finland were attacked (N=53) and the increased threat of Russia (N=32). Even here, the most often used caveat was that Finland should not seek membership in NATO (N=99).
To summarize, opponents of NATO membership don't want Finland to get involved in other people's quarrels, especially ones that concern Russia. Supporters consider membership to be helpful in defending the country against Russia. The first group wants to avoid conflicts; the second wants to be prepared for the worst.
The survey also provided party-wise numbers (with 2006 figures in parentheses):
Ninety-seven (69 %) per cent of Left Alliance supporters are against NATO membership and the corresponding numbers for the other parties’ supporters are as follows: Greens 77 per cent (87 %), Social Democratic Party (SDP) 75 per cent (61 %), Centre Party 67 per cent (72 %) and National Coalition (conservatives) 38 per cent (44 %).
The changes from 2006 are so big that the margin of error must be quite large, but the left-right split is undoubtedly true.