Concurrent with the presidential elections would be the biggest change. Once the block of conservative southern democrats started retiring, voters started returning non-administration majorities in the House in the next midterm election after electing a president, starting in 1994. The only exception was 2002. WIth four year concurrent terms, this stops happening, and I suspect the Democrats even hold the House narrowly in 1996 and 3012, when they lost it IOTL, though the national popular vote percentages to re-elect Clinton and Obama in those years were underwhelming.
If Senate terms are not changed, there are still "mid-term" elections since on non-presidential years, most state governors and legislatures will still face election, along with a third of the Senate. The presidential party might do worse in these Senate elections than IOTL. The presidential party did lose control of the Senate in the 1986, 1994, 2006, and 2014 elections and this still happens, so you still get non-administration control of the Senate in the last two years of Reagan's, GW Bush's, and Obama's administrations, and most of the Clinton administration and all of the GHW Bush administration. Democrats keep control of the House until 2000 instead of 1994.
I don't think non-concurrent (with the presidential election) turns would be adopted, but doing so would affect events less since starting in 1994, control of the House only turned over in the mid-term elections.
LBJ probably proposed the change so that Congressmen would spend more of their time on government and less on campaigning (more strictly, campaign fundraising), and I think that would happen and lead to some improvement in government overall.