The Republicans do have more small ($1000) donors than do the Democrats. This is attributed at least in part to extraordinary efforts at donor list development. While the Republicans have been known to raise more hard and soft money than the Democrats, as a general rule soft money constitutes a larger percentage of the Democrats overall funds--that is, soft money is arguably more important to the Democrats.
As for the impact of the "reform" legislation on the Democratic party, the immediate result is that any soft money the Democrats have on hand will need to be refunded after the elections, or the law requires that it be "disgorged" to the federal government by the end of the year.
The second result is that the fundraising efforts which currently direct soft money to parties will be used to direct funds to certain advocacy groups (most likely 501(c)(4)s, which are non-profits that can lobby). Members of Congress are permitted under the reform bill to do some fundraising for these groups--a concession the black caucus and the NAACP received in order to get their support for the bill. While the law places the same onerous restrictions on advertisements run within 60 days of a campaign on these 501(c)(4)s, no one believes that this part of the bill will survive judicial review. That means that 501(c)(4)s are very strong in the new reform world, and parties become much weaker.