* Optogenetics advantages: don't need to insert things into tissue. Disadvantages: requires genetic engineering that is not approved for human use. Difficulty reaching deep brain targets. To image many neurons, might need to pump lots of light into an area, causing heat and cell death. Bulky.
* Microelectrode arrays (https://en.wikipedia.org/wiki/Multielectrode_array) like the Utah or Michigan array advantages: direct electrical recordings, relatively compact. Disadvantages: low density, invasiveness.
It is worth noting that most behavioral studies are done with MEAs are due to their convenience/form factor.
It is also important to note that these two technologies measure different things: an MEA can record extracellular voltages, so it's a relatively direct measurement of neural activity, compared to optogenetics, which relies on ion channels fluorescing, which is not exactly what most people really want to measure.
A word about invasiveness: when you insert large (>1um) things into tissue, you elicit a foreign body response, starting with inflammation and ending with scar tissue or gliosis. The issue with invasive probes like MEAs is that even if you manage to avoid major blood vessels and you control bleeding and inflammation, ultimately scar tissue forms around your probes. Scar tissue is a much worse electrical interface than plain tissue, and thus the effectiveness of your BCI/BMI implant diminishes.
Disclosure: I run a company (Paradromics, www.paradromics.com) developing next-generation microwire technology for brain-machine interfaces. Also, my strength is in software so while the gist of what I'm saying is probably mostly correct, I can't give details as well as others can.