I've heard that there are compatibility problems when using 50um fiber with some fiber converters. After some research I'm thinking this is a legacy issue when using slower devices (100 Base FX) that used LEDs. I was told that the fiber converters are made for a certain size of fiber core and wont work with 50um fiber. Am I right in thinking this is just a corporate knowledge thing that is outdated when using 1000 Base SX converters (which should be using lasers instead of LEDs)?
Basically they're not remotely compatible and will fail either on day one or pretty soon afterwards if used simultaneously. There are lots of reasons why there are two standards but they're far too dull, there's nothing inherently better or worse technically for each one carrying any kind or speed of traffic but the key thing is not to use the same together. We chose to stick to 62.5u for everything, just so we all knew what everything was - I suggest you decide one way or the other, make a similar rule and stick to it.
There are four types of multi-mode fibre: OM1, OM2, OM3, and OM4.
OM1 has 62.5 um core, all the others have 50 um. The main differences between the others is how much information they can carry, as measured per MHz-km. OM4 was only recently standardized in the last year or so, specifically to help with 40 and 100 GigE over longer distances. The various types cannot (generally) be mixed and matched. If you need to do this the purchase of a media converter is necessary:
Honestly, if you're working with multi-mode, try to stick with OM3 if at all possible. In the long run the material cost is irrelevant as it's usually labour that gets you. Ideally, if you're thinking on stringing new fibre, get a quote for both OM3 and OM4 from your installer and see if the difference is huge or not. If not, it may be worth considering "future-proofing" yourself as fibre often sits around for a decade or so.. OM3 should be fine if your runs are 100 metres or less though.
Beyond that, you haven't actually said what you're trying to accomplish, so it's hard to given specific advice on what you should do. If the question is what you should use with 1000 Base-SX, then 62.5 um will (according to the standard) get you 220m of length, while 50 um should get you 550m.
The basic problem is that you can't use 62.5 and 50um in the same run.
Otherwise, there are some minor advantages of 50um over 62.5 if you're going to be using really long runs of 10gb Ethernet or the equivalent Fiber Channel.
The basic rule of thumb is to use whatever is already deployed elsewhere in your enterprise. If you're worried about 10gig and you've already got 62.5 everywhere and you've got really long runs, use single-mode fiber.
The basic problem is that the patch cables look exactly the same except one is marked (in little tiny letters) 62.5 and the others are marked (in little tiny letters) 50um. And if you accidenatally mix the two you'll get a link and everything will appear to work with trivial volumes of traffic. And worse still, one direction of the link (the 50->62.5 direction) will actually work pretty well, the other direction will work terribly once you put it under load and you'll go crazy trying to figure out why you've got such a "slow" link and why you've got so many errors.
But that's only if you have a single run with both 50 and 62.5 micron. Otherwise, everything up to really long runs of 10gig will work fine with either in almost all situations and equipment.
Whatever you've already got in your buildings or datacenter is fine. If you're building a new deployment, go with 50 micron or better still go with single mode. And lastly, if / when you move to 40gig / 100gig, you'll have to throw all your existing fiber plant out anyhow.