There are two types of seats we're talking about: Democratic seats that went narrowly Republican and Republican seats the Democrats narrowly failed to pick up. Most of the former were conservative Democrats who lost in the South. Most of the latter were seats that would slowly be picked up by Democrats later as demographics overcame the incumbency effect and politics of the moment. Just spot-checking, I'm seeing a lot more of the former within the 2-3 point margin than the latter. This means more southern, conservative Democrats serving a bit longer.
So keeping it basic (and sorry if this isn't interesting) the character of the chamber wouldn't change that much; no additional movement on social policies, no changes to the trend in immigration legislation, no real work on education reform (these are States' Rights Democrats, after all). The two big conservative economic bills in '97 might have been a little harsher on the rich, a little leaner on Medicare cuts. But in general Clinton got economic bills he, as a fiscal moderate, could live with IOTL. He wouldn't have seen it as a victory to vary too much from their substance of tax credits for promoted behaviors and lower taxes on the poor.
But obviously no impeachment. They may have been forced to hold hearings, but with less room for conservatives to run wild with the material. It gives Republicans something to run on in '98 and maybe take back Congress, but probably not a blank check to prosecute a president after the issue had been basically resolved.