I tend to take the view that it doesn't matter. Nevertheless, I have a convention for my own records as follows:
The side which gives generic information (i.e. which is not specific to that issue or denomination) is the obverse. This means royal effigies, the Irish harp, the Soviet arms. By extension I also call the obverse the side with a President's head on it on standard US coins. Although each denomination has a different President, the coins aren't specifically commemorating that President. So I treat the President's head in the same way as I treat the Queen's head on Commonwealth issues.
The side which gives specific information is the reverse. This may not necessarily be the face value, although it often is. On some UK £2 coins, for example, the value is under the Queen's head, but the other side contains very specific commemorative material and is therefore clearly the reverse.
Of course, there are always going to be grey areas, which is why ultimately I don't think it matters. For the 2002 £5 coin above, I take the profile image of the Queen to be the obverse and the equestrian view the reverse. Virtually all British coins have a profile of the Queen, and that profile appears on the obverse, so the obverse it is here.
On Andy's Mauretanian coin it's virtually impossible to decide on objective criteria, whether mine or anyone else's. In such a case I'd go for the side that's most important to me as being the reverse, and in this case the important side is the French side, because I can read French well but can do little more than transliterate numerals and placenames in Arabic.
There are also downright exceptions. Most Soviet coins have the value (with or without wreath) on what I call the reverse and the hammer and sickle and CCCP on the obverse. It seems perverse, therefore, to swap them round for the 1 rouble commemorating the centenary of Lenin's birth in 1970, so the value side is still the reverse in my records, even though by my criteria above Lenin should be on the reverse. Perhaps I'm reinforced in this by the fact that he's represented by a profile bust, which custom tells me is on the obverse from my own country's coins.
I also suspect I'm unorthodox in my use of the terms obverse and reverse. Before I was interested in coins, I'd never come across the term 'obverse' and the word 'reverse' was more often a verb describing something you do with a car than it was a noun (where 'back' would be a plainer English term in most instances). Therefore I did not allocate in my mind a status to each term, although subsequent reading makes it clear that, certainly where the Royal Mint is concerned, the 'obverse' is more important. Because the tails side of UK coins was called the reverse, I simply then called what I deemed to be the tails side of other countries' coins the reverse too. FWIW I always list the reverse description before the obverse in my spreadsheets.
