First, I'll qualify my answer . . I'm an engineer, working the battery business for more than 25 years .. . . more than 15 of my 25 was spent actually designing and developing automotive batteries . . . . up until almost 2 years ago I was employed by Optima, if you've ever been to SEMA and stopped by the booth with questions, I was likely the person that answered them.
I'm not going to try and convince everyone that Optima is the beat all, end all.
DiscoMike is right, the reason you want to pair like tech and age batteries is because in a parallel string, the batteries will always "search" for a level voltage state. You have a much better chance of achieving this by matching the batteries.
The example of the old 24V Military setup is a little different, while an engineer would say it's not an ideal situation to put two different batteries in the series string, provided the batteries are both nominaly 12V you can get away with it, for a period of time before imbalance occurs (unless there is excessive discharge currents).
DiscoMike is also correct that the Odyssey and Platinum come for the same producer. Actually the same plant in Warrensburg, MO. Internally they are identical.
Personally I own a Optima for my Jeep and an Odyssey for my track-day M Roadster. I've not changed out my Rover battery yet as I've only owned the truck for two weeks.
When picking the battery, you really have to ask yourself (and be honest) how the battery is going to be used. Note, the battery ratings are industry standard values (better said, SAE specification attainment values), so use caution when using the ratings as a primary decision factor. For those like DiscoMike that likely use their accessories (winch/off-road lights) more frequently than say, someone using their third row seating, Optima is probably the better choice. It's more tolerant of voltage swings, has overall better high current power (meaning less voltage drop under high loads, ie a loaded winch pull)
For those that are more into dry camping or like to illuminate their campsite with their bank of OR lights, the Platinum/Odyssey would be the better choice. They offer generally better Ampere Hour capacities (ie fuel tank) in the same footprint.
If you blend both of these worlds, I would choose the Platinum/Odyssey as that is likely what I'll put into my LR3. Although, admittedly, I've had my Optima for almost 8 years.
Brief history note, Odyssey and Optima were born out of the same R&D lab in Denver, CO. Their technologies are very similar, although the design/construction approach is different.
Hope you found this to be a non-biased opinion, and I'm happy to field any battery related questions.