LBJ's experience as leader of the Senate involved executive decisions and a whole lot of wheeling and dealing. I hate recommending books but Robert Caro (Master of the Senate) really is indisensible. One could argue - and I certainly would - that LBJ was one of the best equipped candidates who ever ran for president. Reading Robert Caro's description of the Southern oligarchs in the Senate is like reading about something from the Middle Ages.
It was Johnson's political genius that brought about senate reform. Prior to his arrival the place was a museum. It was thanks to Johnson's careful plotting within the senate that the US no longer has segregation with its myriad petty and vindictive restrictions. Yet that was less than 50 years ago. Within living memory!
And yet LBJ could be and often was a vindictive swine. He was also in the pockets of the Texas oil industry and spent a lot of time sucking up to the Southerners.
He was a Shakesperean figure, no doubt. So I would argue that experience is not necessarily a positive indicator of how a presidential candidate will fare in the White House.