Gentiles coming to faith in the God of Israel would have been familiar with the “Two Ways” concept from their own cultural background.
Similar ideas are found in Greek works such as Xenophon’s Socrates’ Memorabilia and Plato’s Chariot Allegory. In fact, the metaphor of choosing between two distinct paths in life was quite common in ancient religion and philosophy. Yet, none of this compares to the plethora of examples and prominence that the two-choices teaching played in Judaism.
In the last book of the Torah, just before Israel was about to advance into the promised land, the LORD set a choice before the children of Israel and told them to decide between two separate paths:
I am setting before you today a blessing and a curse: the blessing, if you obey the commandments of the LORD your God, which I command you today, and the curse, if you do not obey the commandments of the LORD your God. (Deuteronomy 11:26‒28)
The people had been given the Torah, God’s righteous instruction for their lives, and now they needed to choose whether to obey or disobey:
I have set before you today life and good, death and evil. If you obey the commandments of the LORD your God that I command you today … then you shall live and multiply … But if your heart turns away … you shall surely perish. (Deuteronomy 30:15‒18)
The theme of choosing between two ways continued in the Tanach, the literature of the intertestamental including the Dead Sea Scrolls, as well as in rabbinic literature. Therefore, the concept of the two ways in life was firmly rooted within Judaism and filled the pages of its literature. The Jewish disciples of the Master naturally tapped into that rich Jewish tradition when they penned the Didache.
It’s interesting to me to see how the Two Ways concept was developed in later Jewish literature as well, in particular Chasidic thought. On the title page to the Tanya, the famous book of Chasidic philosophy by Rabbi Shneur Zalman of Liadi, we find:
Compiled from (sacred) books and from sages, exalted saints, whose souls are in Eden; based on the verse “For it is exceedingly near to you, in your mouth and in your heart, to do;” to explain clearly how it is exceedingly near, in a lengthy and short way, with the aid of the Holy One, may He be blessed. 
Rabbi Zalman speaks of two ways, one that is long and one that is short. In actuality, the way that is short at first is very long, and the way that is long at first is very short. We find this illustrated in a parable in the Talmud:
I was once on a journey when I noticed a little boy sitting at a cross-road. “By what road,” I asked him, “do we go to the town?” — “This one,” he replied, “is short but long and that one is long but short.” I proceeded along the “short but long” road. When I approached the town I discovered that it was hedged in by gardens and orchards. Turning back I said to him, “My son, did you not tell me that this road was short?” — “And,” he replied, “did I not also tell you: But long?” I kissed him upon his head and said to him, “Happy are you, O Israel, all of you are wise, both young and old.” (b.Eruvin 53b)
What is the short road that is long and the long road that is short? The short but long way indicates a way that seems easy at first but turns out to be hard. A long but short way is a way that seems hard at first but pays off in the long run. Certainly, this can be comparable to the Didache’s Way of Life and Death. The Way of Death seems easy at first but ends up in destruction. The Way of Life seems hard at first but ends up in life.
From the approach of Chasidus,  the two ways represent on the one hand, a person who simply goes through the motions of Torah life and experiences the same spiritual struggles day after day; this is the short but long way. In the end they have no real victory. Then there is the long but short way, where one seeks to infuse the Torah into one’s emotions, contemplating on the love and awe of God, and transforming all this into action. This individual is not just going through the motions and in the end will reach his spiritual destination. It takes work up front but it is worth it long term.
This is further discussed in the Chabad classic HaYom Yom by Rabbi Menachem Mendel Schneerson:
“From G‑d are man’s steps established” (Psalm 37:23). Every one of Israel has a spiritual mission in life - which is to occupy himself with the work of construction, to make a “dwelling-place” for G‑d. Every one, regardless of his station or location, must, through an exhaustive search, seek out a spiritual livelihood with all the intensity of his strength, just as he seeks a material livelihood.
This is so because, (as the above verse concludes) “he desires His (G‑d’s) way.” As it is written of Avraham: “For I know and love him because, etc. and they will keep the way of [the LORD]” (Genesis 18:19). There are two “ways”: The way of nature and the way that transcends nature. G‑d created the universe in such a way that, in man’s eyes, it appears to follow a set pattern of nature; this is the “way” of [G-d]. Torah and Mitzvot are the “way” of [the LORD], drawing that which transcends nature into nature. By virtue of this (conduct of Israel) G‑d endows Israel from that which is beyond nature into the natural. 
While there is way more here than we can unpack in this short blog post, the bottom line is that the short but long way is the way of nature, the natural easier way that people choose, again not unlike the Way of Death in the Didache. There is also the long but short way, which is beyond our natural inclination, which seeks to draw down godliness from above and bring it into the natural order of this world. This is the harder way much like the Way of Life of the Didache.
What the Didache and Chasidus both teach us about the two ways is that it takes hard work to reach our full spiritual potential. The ways of the world call us to look for an easier shorter route but ultimately that leads nowhere. The choice is ever before us and as disciples of Yeshua we must choose the more difficult path, for it is only on it that we will reach the destination of the kingdom.
For more on the Didache check out First Fruits of Zion’s new Messianic Jewish translation and commentary on the Didache entitled The Way of Life: The Rediscovered Teachings of the Twelve Jewish Apostles to the Gentiles.
- Rabbi Schneur Zalman of Liadi, Likutei Amarim: Tanya Bi-Lingual Edition (Brooklyn, NY: Kehot, 1998), x.
- Taken from Rebbe Menachem Mendel Schneerson, “The Longer Shorter Way,” n.p. [cited 12 December 2017]. Online: http://www.chabad.org/library/tanya/tanya_cdo/aid/1117/jewish/The-Longer-Shorter-Way.htm
- HaYom Yom, Cheshvan 14, n.p. (cited 12 December 2017]. Online: http://www.chabad.org/therebbe/article_cdo/aid/5974/jewish/Hayom-Yom-Cheshvan-14.htm.