Okay global versus local clock and why doesn't Beast2/Beauti2 have this option.
Firstly, if Beast2 disallows a global clock ... hallelujah! Finally... Beast1 did allow this option and it was an issue because it was the default option.
A global clock means that all mutations within the tree from the very first common ancestor to the most recent tip (leaf) have taken place at exactly the same rate. So there is one molecular clock that is ticking at the same rate in every point of the tree. Thats not how evolution works, particularly something as prone to epidemics as an infectious disease.
For example, if you have a tree that comprises different epidemics at different times and then for example an endemic sylvatic virus (such as dengue primate virus), the idea that they have all mutated at exactly the same rate does not make sense. Moreover, you can statistically check for a global clock ... and the tests always fail.
A local clock means that there are multiple mutation rates within a single molecular phylogeny. Take the above example, one epidemic mutates at one rate, call it "rate 1", the second epidemic mutates at a different rate, call it "rate 2" and the sylvatic virus mutations at a third rate, call it "rate 3". Thus one tree has three "molecular clocks", or "local clocks". This approach where one "clade" (monophyletic group) comprises one rate is called "autocorrelation". However, an epidemic could contain multiple rates molecular clocks and those rates could have identity to the other epidemic, i.e. an epidemic comprises a series of rates similar to gears on a car. The epidemic gets started ("rate 1"/ "gear 1"), gets into "log-phase" ("rate 2", "gear 2") , then peaks ("rate 3"/ "gear 3") and that process could be identical between different epidemics. Whatever the model if you are attempting to obtain a molecular date by ignore three profoundly different mutation rates, I think you can agree - it will never work.
Any Beast model calculates all those complex clocks (except for the global clock option) without the user needing to think about their complexity. "Lognormal model" is the most widely used and most robust, but the "exponential model" (I think thats what it's called) might be of value for a dengue virus epidemic. Both those models estimate molecular dating.
However, I think you can see the idea of just assuming a single global rate, doesn't make rationale sense and again statistically its rarely observed for an entire phylogeny.
Using Beast to obtain a phylogenetic tree with robustness scores with dengue virus is a good idea. However, performing molecular dating for any flavivirus is a specialist area, undertaken by experts in virus molecular dating. Just the variety of different models alone is just one issue. The level of cross-validation is a second issue and so on...
Getting a robust phylogeny however is a very good use of Beast and easy to do without error.
Note If you have other Beast questions I'm happy to answer them as separate questions. The site format is that one question is posted per technical inquiry.
Final note The other parameters, eg. mutation models, between a local and global clock are the same. The key parameter is of a global clock is taking the total genetic distance between two taxa and assuming the "node" (common ancestor) is exactly the mean of that genetic distance. Thats the technical model it uses.
From the comments A strict clock is a global clock, it's the same thing. Just to be clear on its usage okay if you are using it to demonstrate a tree topology, but thats it, definitely not for molecular dating (Beast output comprises both outputs). Global clocks tend to give weaker support for a tree topology, but thats okay, because if it supports a branch then every other Beast model will.