Which timing of mincha is more important: mincha gedolah or mincha ketana? Why?
There is an advantage to praying Mincha Gedola (mincha between 6.5 halakhic hours into the day and 9.5) as "Zerizim Makdimim L'Mitzvos" (alacritous ones are early to fulfill commandments). There is also an advantage to praying Mincha Ktana (from 9.5 until the end time (10.75 or 12)), as mincha k'tana more accurately projects the time of the Korban Tamid Shel Bain Harbayim.
Same answer as Gershon, just with more English:
"Mincha gedola" (earliest mincha) is 12:30PM assuming 6AM sunrise 6PM sunset. It's the earliest time for Mincha.
"Mincha ketana" is 3:30PM on a 6-to-6 day. Theoretically the ideal time to say mincha is mincha ketana or later; however, often schedules work out that it's better to get it in earlier, in which case "mincha gedola" is great. (Some tradeoff between doing the mitzva sooner and better.)
There's also some discussion about what activities you shouldn't start before davening Mincha (e.g. sitting down to a [big?] meal); depending on the conclusion of that discussion and your daily schedule, mincha gedola might again be a good idea.
There are conflicting opinions in the Rishonim as to which of these time periods is the preferred choice for davening Mincha. Some Poskim, Rabbeinu Seadya Gaon, Rif, Ritva, Rosh, Tur, prefer Mincha Gedola, while Rabbeinu Chananel, Rambam, Archos Chaim, Meiri, hold that Mincha Ketana is the preferred time to daven. As there is no decisive ruling on this question, either custom may be followed.
Rav Yitzhak Yosef in Yalkut Yosef 233:1 holds that praying Minha Ketana is better. However, those that Daven Gedola have authorities to rely upon.
Davening at minchah gedolah is okay, but not ideal — except that there are factors that will make minchah gedolah a preferred time. Availability of a minyan, how busy your afternoon usually is, the likelihood of forgetting to daven if you wait for late afternoon — these are some of the factors that prompt people to opt for a minchah-gedolah minyan.
Each person must know himself and take steps to avoid the inadvertent missing of Mincha. Often this means davening Mincha before settling down to a long afternoon and early evening of work.
—R' Phil Chernofsky. Torah Tidbits: Special Features for Parshat Chayei Sara. 25 Cheshvan 5759.
At the time youll be able to daven best and feel most connected to hashem seems to be the answer to aniyus daati