It's worth pointing out that having a Senate based on states not population is not unique to the US, Australia does the same thing. In Australia, the 6 states get 12 senators each, and the two self-governing territories get 2 senators each. This means that Tasmania (with a population of 539,590) gets 12 senators – 1 senator per 44,966 people – whereas New South Wales (with a population of 8,157,735) also gets 12 senators – 1 senator per 679,811 people. So a Tasmanian's Senate vote is worth 15 times as much as that of a New South Welshman such as myself.
On the other hand, we do use proportional representation (single transferrable vote, STV) to elect the senators for each state, which is different from the first-past-the-post method the US uses. In a normal election, half of a state's senators are up for re-election; exceptionally, the government may call a special "double dissolution" election, in which the whole Senate is re-elected, if the Senate repeatedly refuses to pass legislation sent to it by the House of Representatives. Our use of STV means that minor parties (Greens on the far left, One Nation on the far right, various centrist/populist independents and other small parties) end up controlling the balance of power in the Senate. Some people don't like that because these minor parties end up sometimes extracting all kinds of concessions from the government in exchange for letting government legislation through.
I think some kind of unequal representation – like the Australian and US Senates – is essential for a federal system to work. Look at the United Kingdom – England has almost 85% of the population, so a big enough majority in England can always overrule the other three smaller constituent countries (Scotland, Wales, Northern Ireland), and there are no constitutional mechanisms to prevent that from happening. That's a large part, I think, of why the UK looks like it isn't going to last, with Scotland likely to break away sooner or later, quite possibly followed by Irish reunification some years further down the track, and once its just England and Wales, maybe even Wales will eventually decide to follow Scotland's example. If the British House of Lords was more like the Australian and US Senates, and gave the smaller constituent countries the ability to block an English-dominated majority, then the UK would be more likely to survive.