The House of Representatives is the more powerful of the two houses, able to override vetoes on bills imposed by the House of Councillors with a two-thirds majority.
How did the LDP end up with massive majorities in the lower house and not be close in the 'Senate'? I presume that the Councillors is Senate like in terms of population inequality but it looks like they try to partially correct for this by giving Tokyo and such extra Councillors.
Elections for each house are separate. The House of Councillors is elected by halves, with the last two elections in 2007 and 2010. There's another election this year, where the majority of seats up for reelection are DPJ-held. In 2007, the LDP was
persona non grata, and the DPJ (and allies) won 65/121 seats to 46/121 for the LDP/NKP alliance (the balance was won by the Communists (3 seats) and various independents, mostly of the anti-LDP variety). In 2010, the LDP did better and gained some ground, but the DPJ was still the largest party (though the LDP won the most seats of those up in 2010).
The House of Councillors is not at all "Senate-like". It's supposed to be properly proportionate in distribution but suffers from the same redistribution inertia as the House of Representatives. It also has weird multi-member seats in some places and has basically the same kind of extra proportional list seats that the House of Representatives has.