Out of curiosity I looked at the cards of a number of east Anglian courses on which match play is the norm, with a particular eye on fousomes (alternate shots).
Hunstanton has par 3s at the 4th, 7th, 14th and 16th, and par 5s at the 2nd, 8th, 9th and 15th. While the par 5s offer no particular advantage to the driver of odds or evens, the par 3s are mostly on evens. As the 14th is a 219-yard monster played blind over a distant hill and needing a fullish carry, perhaps this hole will decide which player takes odds and which evens, although it is fair to say that the hardest drives all come on odd numbered holes 1, 9, 11, 15, 17.
Similarly Royal West Norfolk has three even numbered par 3s (4, 6, 10) and one odd, 15th. The par 5s come at the 7th, 8th and 11th. As they are not hugely long (longest 492 yards) they are not a major factor. There are critical drives on the 8th and 9th, so both players have to be competent in that area. but he who plays second at the 8th (a time of decision about whether the green can or cannot be reached from an island fairway) also drives at the 9th, perhaps my mind is already being made up.
Royal Worlington is a 9-hole course, so second time round the turns are reversed, so there are no critical decisions to be made - each of you has to face up to the difficult shots once in the round.
Aldeburgh, another very traditional club, has no par 5s, but a number of very strong long par 4s. The short holes come at the 4th, 8th, 15th and 17th, so honours are even there. This is a pretty good test of long, accurate driving, and I reckon that the better driver might be well emplyed on the odds, with the 1st, 3rd, 5th, 7th and 11th among the sternest tests. However, the 6th, 10th, 16th and 18th are not far behind in driving demands. The more I think about it, this may be one of the best foursomes courses in the country - there is nowhere to hide a weaker player..... Walker Cup anyone?