Recently I wrote to my representatives in the European Parliament about software patents. (My message was, `vote for software patents and you lose my vote'.)
MEPs used to be elected by the first-past-the-post system used for Westminster MPs, but with much bigger constituencies. (There are 87 UK MEPs, one for every 675,000 people, compared to 659 MPs, one for every 90,000.) Now they are elected using single-transferable-vote on a party list.
This means that in each `region' of the UK, there are a number of MEPs, who collectively represent the region's citizens. In the Eastern Region (East Anglia plus a bit), there are eight. If you want your representatives to know your views, you have to do a mail-merge and post eight letters. (In the South East region, there are eleven MEPs.)
So at the most basic level, lobbying the European Parliament costs much more than lobbying the Westminster Parliament. This may seem trivial -- a stamp only costs 28p -- but inconvenience is important. I'd never thought about this effect when pondering electoral systems. Here's a different take on it, from the 1998 Report of the Independent Commission on the Voting System, discussing the Republic of Ireland:
101. It was also suggested that the constituent with a grievance does not so much go to the TD [Teachta Dála, member of parliament] of his choice as go in turn to all three or four or five of them, according to the size of the constituency in which he or she lives, thereby wasting a good deal of the time of ministers, civil servants, TDs, and indeed of the constituents themselves.
-- note the order in which the various people are listed.
But a grievance is different from an opinion. If I have a grievance, probably a single MEP could address it -- or, if not, try to persuade their colleagues to assist. But if I want to influence the outcome of a vote, I'd be foolish to contact only one MEP, since (a) my opponents are probably less scrupulous; (b) there's no sensible way to choose just one.